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In Star Wars Episode I: The Phantom Menace, Queen Amidala tries to tell the Senate that Naboo is being invaded, but her claim is called into doubt by a Trade Federation representative.

Queen Amidala: Honorable representatives of the Republic, distinguished
delegates, and Your Honor Supreme Chancellor Valorum, I come to you under
the gravest of circumstances. The Naboo system has been invaded by force.
Invaded...against all the laws of the Republic by the Droid Armies of the
Trade...

Lott Dodd: I object! There is no proof. This is incredible.

As "How it Should Have Ended" pointed out, Queen Amidala had a great deal of proof:

• Video evidence of the Trade Federation attacking their ship as they left Naboo


• Video testimony of the governor of Naboo, Sio Bibble, telling the Queen that people were being killed by the Trade Federation's droid army (sent after they had left the planet)


• The personal testimony of multiple witnesses, including two Jedi (who, as the opening crawl tells us, were dispatched by the Supreme Chancellor to investigate this very issue)

Why was none of this brought forward as proof that the invasion was occurring?

There were no third-party, independent accounts of the invasion - just the word of the ruler of a planet that was having a dispute with the Trade Federation. If we look a little further in the script:

LOTT DOD (delegate from the Trade Federation): I object! There is no proof. This is incredible. We recommend acommision be sent to Naboo to assertain the truth.

VALORUM: Overruled.

LOTT DOD: Your Honor, you cannot allow us to be condemned without
reasonable observation. It's against all the rules of procedure.

A third box representing Malastare moves into the center of the room. AKS
MOE, the Ambassador, addresses the convention.

AKS MOE: The Congress of Malastare concurs with the honorable delegate
from the Trade Federation. A commision must be appointed...that is the law.

Notice that nobody's saying that Padme's accusations should be ignored or forgotten, but that they must be investigated by an independent commission. Yes, such a commission would have found that the Trade Federation had invaded illegally - if it ever got off the ground, with Palpatine slowing everything down.

This is what was meant earlier in the film when Sidious was talking to Gunray:

DARTH SIDIOUS: Good. I have the Senate bogged down in procedures. By the time this incident comes up for a vote, they will have no choice but to
accept your control of the system.

Most of the evidence the Queen has with her could easily be fabricated; the only independent evidence she had was the testimony of the Jedi, and they weren't there. If she'd been thinking clearly, she probably would have called them, but she wasn't thinking clearly. She had been carefully prepped and manipulated by Palpatine:

PALPATINE: ...the Republic is not what it once was. The Senate is full of
greedy, squabbling delegates who are only looking out for themselves and
their home sytems. There is no interest in the common good...no civility,
only politics...its disgusting. I must be frank, Your Majesty, there is
little chance the Senate will act on the invasion.

AMIDALA : Chancellor Valorum seems to think there is hope.

PALPATINE : If I may say so, Your Majesty, the Chancellor has little real
power...he is mired down by baseless accusations of corruption. A
manufactured scandal surrounds him. The bureaucrats are in charge now.

AMIDALA : What options do we have?

PALPATINE : Our best choice would be to push for the election of a stronger
Supreme Chancellor. One who will take control of the bureaucrats, enforce
the laws, and give us justice. You could call for a vote of no confidence
in Chancellor Valorum.

AMIDALA : He has been our strongest supporter. Is there any other way?

PALPATINE : Our only other choice would to be to submit a plea to the
courts...

AMIDALA : There's no time for that. The courts take even longer to decide
things than the Senate. Our people are dying, Senator...more and more each
day. We must do something quickly to stop the Federation.

PALPATINE : To be realistic, Your Highness, I'd say we're going to have to
accept Federation control for the time being.

AMIDALA : That is something I cannot do.

Palpatine has prepared her to see the exact situation they do see - squabbling senators, no interest in the public good, a request that she delay and let her people suffer...so she moves forward with the dramatic move nobody (except Palpatine) had expected.

EDITED TO ADD:

I forgot to address this when I first answered, but the description of the Jedi's mission from the question:

The personal testimony of multiple witnesses, including two Jedi (who, as the opening crawl tells us, were dispatched by the Supreme Chancellor to investigate this very issue)

...is not correct. The opening crawl says:

While the congress of the Republic endlessly debates this alarming chain of events, the Supreme Chancellor has secretly dispatched two Jedi Knights, the guardians of peace and justice in the galaxy, to settle the conflict.....

The Jedi were sent to negotiate the end of the blockade, not to investigate reports of a Trade Federation invasion. The testimony of the Jedi would have helped strengthen Padme's case, certainly, but it would not have been the same as sending a commission specifically to see if there really was an invasion.

First of all this is politics. Even in a galaxy far far away, there are alternative facts.

Second, communications were cut. This means it was particularly difficult to get news from the planet. Few sources are easy to fake, few informants are easy to deny. Especially when proofs come only from the accusation side. There are clues but it is all about being convincing. For some reasons, not everybody trust Jedi.

The second part of your question was addressed by Steve Sansweet, (former) Lucasfilm Head of Content/Head of Fan Relations on the old "Ask the Jedi Council" feature on the official Starwars.com website.

In short, the Jedi involvement was a secret. Chancellor Valorum was worried that if Qui-Gon and Obi-Wan testified about the blockade, presumably the next question they would be asked is "Why were you there and who sent you?" the answer to which ("We were there to pressure the Trade Federation into ending the blockade at the secret behest of the Chancellor") would result in a massive political row.

Q. Why didn't Qui-Gon and Obi-Wan testify on the Queen's behalf during the senate hearings? They had proof of the Trade Federation
invasion. They were there!

A. In the opening crawl to the The Phantom Menace, you'll note that it specifically says that "Chancellor Valorum has secretly
dispatched two Jedi". There's the key word: secretly.

The Jedi didn't testify because they weren't really supposed to be there. ("The chancellor should never have brought them into this,"
says Sidious). Valorum, knowing full well of the Senate's
inefficiencies, didn't bring the matter of sending Jedi ambassadors to
a vote. So, he took it under his own authority to send the Jedi to
Naboo.

Already mired in "scandal and baseless accusation," Valorum couldn't bring up the unauthorized Jedi mission for fear of political
recrimination. As it turned out, Valorum was ousted from office
anyway, and the Jedi were preoccupied with Qui-Gon's claims of finding
the Chosen One of ancient prophecy.

_{^{Starwars.com - Ask the LucasFilm Jedi Council}}

There are at most 3 independent witnesses to the invasion, two Jedi (one of whom is still a padawan) who may have been bought off or have ulterior motives for their allegiance and a Gungan of questionable intellect who would likely say whatever he is told to. Video evidence can easily be fabricated and the loss of communications can be faked.

It is far from unreasonable to request that the situation be investigated by an impartial commission before deploying a military force strong enough to fend off a full scale invasion.

Imagine the egg on the Senate's faces when they have to explain to the public how millions of credits were wasted because of a petty squabble on some far off planet. I for one would demand the immediate resignation of my planets' representative!