2001 Prius engine starts and runs for a few seconds and then bucks and stalls.

Sounds like a classic, sticky throttle plate:
Cleaning Prius Throttle

Bob Wilson

 

1. Clean the throttle body interior and throttle plate, because this is a good thing to do.
2. Disconnect the 12V battery negative cable for a few minutes to let the hybrid vehicle ECU reboot.

While I owned the 2001, I also had experienced occasionally the engine balking symptom that you described in your OP. I think this is because MG1 is not rotating properly, thus fighting the gasoline engine rotation.

 

You could start the car and immediately switch to reverse and see if you can drive it to rule out MG1 issues.. (not sure if this works)

 

Well since you've ruled out a sticky throttle plate and getting an OBD scanner:

• check the fuel pressure - use a gasoline pressure gauge, available from local auto store
• check the spark plugs and wiring - be sure to inspect for wear
• check or replace all vacuum hoses and tubes
• clean the fuel injectors - remove and/or replace
• check the compression of each cylinder - checks for valve problem
• verify fuel - make sure no one slipped in some diesel by running sample in lawn mower

If these simple tests are unsuccessful, replace or rebuild the engine. Simply remove it from the car and take it to your work shop. Then using Toyota shop manual, disassemble and measure all parts for tolerance. Replace the worn parts and all seals. Reassemble; re-install, and; test.

Remember to not cheat and get a Prius compatible OBD scanner that might read out the specific problem. Also be sure to reuse the throttle body without cleaning . . . or buy a new replacement. It is more fun to follow traditional car debugging and diagnostic processes and procedures as these will keep you busy and solve the problem of too much ready cash.

GOOD LUCK!
Bob Wilson

 

Let's say the transaxle had an issue. There is no clutch or anything, and MG1 has to spin, there is just the dampener clutch like disc, right? So the engine might run ok, but let's say MG1 bit it, or a chain sprocket broke off... ? yes/no