What was the plug wet with? Coolant? Fuel? Sorry, but when dealing with vehicle maintenance issues, need really discriptive feedback.
Assuming wet with fuel, sounds like you have a working fuel source. And you said you have spark (ignition). Probably should check for compression. If the timing belt jumped, your compression will be particularly low. 5S-FE engines, if someone replaced the timing belt and was not particularly precise, could cause a later jump, which would affect the timing of the ignition and valve operation, causing a no-start.
That relay you say is missing, if it is the fuel pump relay, it likely has a jumper in the socket. If so, for a 5S-FE engine, this is normal. The 3S-GTE turbo engine had a fuel pump relay in that socket in 1992, but other Celica engines did not.