Scan for codes to see if the computer knows anything about it.
You'll find proceedures for jumping the test connector and counting the 'check' light flashes.
http://www.cygnusx1.net/supra/library/TSRM/
A TPS can cause some of those problems. I just replaced one today for a guy. $75 my shop cost from Carquest. Fuel pressure drop can cause hard starting. Test fuel system per TSRM.