Silk: the way he said it, I'm assuming he cranked it for a while, which would mean that the battery is dead. So the starter works just fine.
It could be anything, really; fuel pump, coil or other ignition component, injection system, or even just a fuse. As far as I know, it is quite rare that the injection system ever has problems; the fuel pump is a more common problem (they just wear out after so long). There are ignition components which will also fail after a while.
One of my brothers had an '86 Celica, which is the same car, pretty much. He did have problems at one point which were very similar to yours, if I remember correctly. I'll have to call and ask him what he did to get it going again.
In the meantime, if you haven't already, hook a battery charger up to the battery and charge it back up. Can't really do anything if the battery's dead.