120a fuse was bad. I got this problem before I replaced engine. Was hoping after replacing it will be fixed, but not. Dealer did not perform any test on my car after engine was replaced, so I would not recommend to do it until all tests are done.

I found few post with similar problem. Interior lights doesn't work, windows, sun roof, radio, something else, but no one found a problem. At least this is what was wrong in my car. 120a fuse located after 2 wires are connected to the fuse box on left side (if you are standing in a front of the car). This might be a helpful for somebody in future

Replaced fuse, drain battery with cranking, charged battery, pull with another car again and wrooooon. It's running now. So, 4 port engine and 6 speed transmission combination, I would say weird, but it is running for now.
Have check engine light on, one of spark plugs not working properly, one of vacuum hoses leaking, car shutting off when it is warm. That might be a reason, or probably will have to replace exhaust, because pipe near old engine have sign of melting. Maybe something is blocking free exit of gases.
So, I do not have time to respond to every post here, or make any comments about "huge f*** failure" as somebody said. I am not intended to read some BS. I start posting here in purpose to get some help or advice from people who knows about rx8 more than I do.
Maybe eventually I will have to look for right engine, but cannot say for sure until I test the car on highway.
Please, if somebody want to say "what a huge mistake" or something like that, keep your thoughts with you, they are not going to help anybody, and I do not think that somebody want to read them here. But if you want to say something interesting, go a head a do that.
Car is running, I have pictures, I have video to prove it, there is difference in engines, however I did not noticed difference in performance just yet. Will keep you updated if it work out good for me or not.

try to go to the auto parts store to get a list of the codes that came up on the check engine. also see if a local member can take a look at the car to see if it is going in to limp mode or if there are any issues that can be easily figured out and resolved...if you can document everything and show how you did it, i will be doing the same thing you did; 4 port engine on 6 speed manual transmission