Okay, so I fixed the issue on my own. I actually had two issues that took me a while to figure out, but for future reference in case someone does a search on this same problem, here's what happened.
I downloaded and reinstalled the COD WAW Tools, overwriting everything I previously had.
Then I tried to compile my map again, until this popped up in the little compiler window.

I said to myself, "Looks like a hint!"
I went to C:\Program Files (x86)\Steam\SteamApps\common\Call of Duty World at War\map_source
Opened up my .map file in Notepad++.
I changed the value to the right of "classname" to "worldspawn" because it was something else.
I now have a worldspawn again.
I tried compiling, but got yet another error saying one of my reflection_probes were halfway through a solid object.
So I went back to Radiant and opened my map, and input the coordinate the compiler error gave me.
Alas! There was the reflection_probe halfway through a wall! I quickly moved it and saved.
Tried to compile again and... it worked!
Map is now functional.
So if you guys run into an error stating that it failed to execute cod2map and/or linker_pc, and closing all programs, changing administration privileges, or restarting your PC didn't fix it, try to reinstall the COD WAW Tools and then try compiling again. It should give you a more detailed error report. Mine was the worldspawn and the reflection_probe. Yours may be different. Give it a go!
You can post this thread as "solved" and something to possibly link to in the future for such problems.