Limp Mode or Something Else?
 

I have recently purchased a 93 rx7 fd. The radiator had cracked on it so the person I bought it from purchased a radiator for me to install. It was a slow leak, so I filled up the antifreeze and drove it a couple blocks to have the radiator installed. While driving it the CEL was on and it kept cutting out and wouldn't accelerate past 2500 roughly RPM, which I figured was because of the radiator issue. I had the new radiator installed, got home and reset all the codes. However, the same issues keeps coming up. When I start it, it starts up with no CEL and I can rev the engine while in park or in neutral. However, once I start accelerating past 10-20% acceleration on the accelerator it cuts out completely. If I try to push the accelerator down more it just cuts out and dies eventually. I tried to check the CEL codes but am getting none. I have a Snap-On Stylus Pro and it didn't pull any codes. I tried the wire from TEN to GND and still no codes. It seems like it is in limp mode, however if I depress the accelerator at roughly 10% it will accelerate to around 4000 - 4500 RPMs before bogging down. Any help is appreciated as I'm running in circles trying to figure out the problem.

Welcome to the board. :)

Only thing that comes to mind is have you checked if your MOP is working?

Here's a link to a downloadable FSM: Foxed.ca

If the CEL is on, there is a code. I'd check again jumping the TEN to GRN. This is an OBD I car, No code reader will work AFAIK.
Limp mode is simply a condition where the ECU will not advance spark and will cut fuel whenever vacuum is NOT present. So any load on the engine...and certainly any boost, will cause limp. But you can VERY slowly accelerate in the lower gears to 'limp' home, you just won't have any power. I think I managed 45 mph once on a flat stretch of interstate with a tail wind while in limp. It just took me about 2 miles to get to that speed. And sitting in neutral you can raise the rpm slowly as long as vacuum is sensed in the manifold.
Your description does sound like limp mode and as diabolical mentioned, a common cause for that is one of three codes related to the MOP (or OMP). But there are other possibilities. It has nothing to do with the radiator.

Thanks for the information, it's much appreciated. I will test the MOP and go from there.

I have tried pulling the codes. I put a paperclip from GND to TEN and turned on the ACC and the CEL just turned on and stayed on and didn't flash. I then took a LED light and placed it on TEN and GND with the ignition on and it just stayed lit up, it didn't flash any codes either. The CEL doesn't come on when the car starts, it only comes on once I begin driving it and get it over 2000 RPMs then it comes on and goes into limp mode and the CEL stays on but once I turn the car off the CEL goes away. Would I be able to check the codes with the car running by chance?

Okay I will try doing that when I get home this evening and let you know if I get anything. Thanks for the information.

Also, as I recently learned there are certain critical codes like Metering Oil Pump (MOP) that even if you resolve the issue and the check engine light and code go away- the ECU remains in limp mode until you reset the ECU by removing the battery terminal and pumping the brake.

If you're following the instructions in that link I posted...and IN THE ORDER set out, then I don't know what to suggest other than networking with someone local to try another ECU or buying a known good one. Many owners (like myself) have installed aftermarket programmable ECUs but have the stock ECU tucked away somewhere.
But if you're getting a CEL while driving the car and what certainly sounds like limp mode, then there is a code.