** Solved **
I did search, and there are a lot of threads(249) to go through, so I figured I would put this up while I skim. So here's the skinny:

I put a 95 B18C1 in my 95 Si. Easy swap and have done a couple of these. The car ran before I swapped it, but now the fuel pump isn't coming on. The main relay isn't clicking. I have an s300 plugged in and I'm pretty sure the ecu isn't getting power because it will not let me upload maps.

Here's what I've tested so far:
- main relay (good)
- ign. switch (good)
- two fuses, the 15 and 7.5 amp fuse underhood (good)
- one fuse, 7.5 amp under driver's dash (good)

Any advice would be awesome! Thanks.

 

Check 15A hood fuse 31 and 15A dash fuse 24.

 

 

I tested all the above and they check out.

 

 

Unplug main relay.

Turn key to ON(II).

In connector, jump pin 1 or pin 5 to pin 7. Does the fuel pump run?

 

Okay, pin 1 to 7 runs the fuel pump with ign off. Pin 5 to 7 runs fuel pump in key ON(II). BUT, now when I plugged the relay back in and tried it again, the fuel pump runs, but the 'battery' light is blinking and the speedo is bouncing around.

 

And now the ecu turns on also. I was able to access the sensors. It says the voltage is bouncing around between 8v and 10v, but I put a multimeter on the battery and it is 12.4v

 

Does the engine start and run?

 

Nope! It doesn't turn over or click. Thinkni should replace the battery?

 

Does the starter crank? Fully explain the current situation.

 

So, I went to go record a video and it turned over and started! The only I did from the last time I tried what you suggested was: a) Put a charger on the battery and b) Put another ground strap on the transmission. I'm not sure which one solved the problem, but I'll take it.