ZDoom

I keep having a problem with doom, and also Zandronum, which someone told me uses part of the engine from Zdoom, that every 20 or so seconds it will go through a major freeze up in doom most of the time resulting in my death, which really sucks. This happens in servers, single player, mods or no mods, I even tried another Iwad besides Doom2.wad. It just keeps happening. Sometimes uninstalling and reinstalling Zandronum is a temporary fix, sometimes not. It keeps happening and I can't play at the current state of things.

cl_capfps 1 ?

I think this is hardware related. Or maybe some bad driver. Regardless, there's nothing in the engine that can be done.
Maybe cl_capfps helps by reducing CPU load but that's merely a workaround, not a fix. The underlying problem would still be there.

In the past, regular freezes similar to the one you describe have been traced to another program running in the background that does something every X seconds. So check to see if you have something running that might cause the problem.

Nope, nothing running in the background that could impede the progress of the game. It happens regardless of capping the fps as well.

Is your graphics card overheating?