When it started did it run normally or rough? If rough, check the ignition timing with a timing light and possibly the valve timing (belt). Check engine codes and clear them by removing the EFI fuse for a minute. If same codes rerurn then the problem is real. If the CPS has been removed it has to be inserted following the manuals procedure. Make sure the air flow meter is dry (and plugged in) and never clean the part that goes inside the housing with any solvent. It can be easily ruined. Check for fuel flow by connecting fp and B+ in the diagnostic block behind the battery with the ignition in the on position.
You should hear fuel flowing that stops when the jumper is pulled.
Here is a link to the online MKIII manual.
http://www.cygnusx1.net/Supra/Library/TSRM/MK3/