RB25 S13 issue/dead/over heat?

[Redr35]

New here and have a question to see if the powers of more intelligence here may help. I picked up a swap RB25 S1 into a S13 and owner didn't run it in a while and said last time (few months ago) it ran for 10-15 minutes then died. And sat. Today I charged the battery and went to start. It turned over and ran, idled fine, after 5 minutes shut off and was completely dead. I filled the coolant all the way figuring it may need some and it did. Car was dead still so I charged and jumped it turned on and started to drive. About 4 miles of driving around my area it just died. Dead, and shut down. When it does this it runs and idles smooth and then just slowly keeps down till it is off. Even if I smash the pedal down it it doesn't matter it hesitates momentarily and then dies.

Just trying to see if anyone knows of anything or an idea of what is happening. I will start trouble shooting wires tomorrow as I have no idea how the swap was done. But would like an idea of where to start possibly. I feel two issues are happening and if I don't have to purchase a new wire harness that would be great.
Thanks in advance.

[2_Liter_Turbo]

I would definitely pull the plugs to see what they look like, it's a good start. Checking the grounds and harness in general is also a good start. I'd also do a compression check. You need to see where you stand overall since you have no prior history with the setup.