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I think you might have some separate issues going on, but let's address the more pressing issue of no throttle response first:
There is a 10 amp fuse in the under hood fuse box labeled ETCS. Check to make sure that fuse isn't blown.
The ETCS fuse powers the throttle control system and almost always blows when jump starting. If it's blown, replace it and then try to start the engine normally and see if the throttle response has come back. From there we will need to see what the remaining symptoms are.
It's possible that the battery or alternator could be going bad and causing the electrical hic-ups that you described, but we really need to get it running again to be sure.
I'll check back in this evening to see if you have additional questions.
Still no throttle response?
I assume the check engine light is on?
Is there a chance that the gas pedal was being pressed the first time it was jumped? This may have re-learned the throttle position to the wrong spot on accident.
It is a definite possibility that the timing belt could have jumped. They will occasionally do that on the sienna.
I just wanted to check and see if you need any additional info.