VoltronMudkipz

Im new here so please excuse me if im too much of a noob.
I looked at a few other posts, and I couldnt find an answer to my problem.

So I have a 88 rx7 convertible, but its completely swapped with a 91 engine, transmission... everything. My problem is that when I try to start the car, it wont get any power, not even turn over. I just recently got a haltech elite 1000 installed by a rotary shop about two months ago. I tested the battery, and it only put out 4cca, so I had oreillys recharge it. However when I went to start it, it didnt even get cluster lights or anything. I checked the engine fuse, and thats fine too. Also, about two weeks ago, the shift buzzer started to randomly go off from time to time, around 3k rpm when I would be cruising. Anyways, the car isnt even humoring me and attempting to start. Weirdest part is when I gave up, and came here, the alarm engaged when I locked the door, and the interior lights began to work.

This happened two days ago, but I tried to deflood it by holding my foot on the gas, and turning it over, and boom problem fixed. Didnt work this time.

Any help would be appreciated.

Thanks!