I am not sure if it makes any difference to your statement, but these cars actually have timing chains, rather than timing belts. Toyota used chains on a lot of their cars before the mid 1980s. Here is a little diagram of it that I found by looking up 82' Celica:
http://www.1982celica.illusionfxnet.com/parts/Tool%20Engine%20Fuel%20Group%2082%20Celica/13-03%20TIMING%20CHAIN%20FIGURE.gif

Not to steer you away, that is the last thing we want to do, but you may want to try one of these forums for more information. This is a Mercedes forum, so may not be too many here familiar with Toyotas, so here are a couple of Toyota forums you may want to try. The first one specializes in Celicas:
http://toyotacelicas.com/forums/
and here is another for Toyotas in general:
http://www.toyotanation.com/index.php?

At any rate- it sounds like the fuel pump has went out. I have owned several Toyotas, but never had a problem like this. Was the car running fine before? Did it stop all of a sudden? Good luck.