Need help- car won't crank, read for details

[rva240]

So my 1996 s14 won't start. The engine does not turn over, but it did start up when my buddy and I push started it, so i don't think it's a performance issue. I just put in a new battery and a brand new starter. I tried replacing the ignition switch as well, but that didn't do anything. The last couple months that my car was still running, sometimes when I would turn the car on, I would turn the key and hold it in the on position, and nothing would happen for about 2-3 seconds, but after those few seconds, the car would start up like normal. A couple times it even took multiple tries of holding the key in the on position for many seconds at a time, until finally, it starts. This mainly happened from a cold start. Then one cold morning, I went to turn the key, and nothing. Any suggestions whatsoever would be greatly appreciated, I can't go another day without driving my car!!

Thanks, Alex

[Infinitiguy19]

Check the ECU and switch it out with a known good one.

[Razi]

Does the starter relay click when you try to start it?