Here is a link to the online MKIII manual.
http://www.cygnusx1.net/Supra/Librar...spx?S=FI&P=108
Check the engine error codes and clear them by pulling the EFI fuse for a minute.
http://www.cygnusx1.net/Supra/Librar...ection=FI&P=23
Check that there is 12-14 volts at the battery. 10 volts or less means a dead cell.
Check the operation of the "main" fuel relay (its the round one in the fuse box behind the battery).
Check for any blown fueses like the EFI fuse or the 30 Amp square one. If necessary check the circuit opening relay located in pasingers side kick pannel. Its described in the manual. you will need a volt/ohm meter and some alligator end jumper wires.