Why does Apple Hardware Test return -6002d error code?

I'm having a terrible time with my 2011 Mac mini. It was having intermittent kernel panics, and at other times it would just dump me to a screen that said my computer had encountered a problem. Other times I would come into the room to find it had rebooted and was at the login screen. I'm unable to find a common thread in the console logs. I've tried removing Parallels (because it loads KEXT extensions to the kernel) but nothing worked.

Eventually, I tried the Apple Hardware Test, and it would come up, then I would start the test and it locked up and had to be rebooted. Eventually, I tried removing one of the memory sticks (I upgraded the machine to 8gb shortly after I got it this spring). It seems that one of the sticks has caused the problem. When I put it back in, the computer even corrupted my hard drive, to the point that it was unrepairable and had to be wiped and reloaded.

Now, I want to test the current setup using the 1 stick of memory that I think is good, but when I try to run the AHT, it just returns "www.apple.com/support" and then an error code of "-6002D." When I was able to run the test, it asked for information to log into my wifi network. Now, it doesn't even do that, it just goes directly to the URL and error code.

I've tried the following: holding down "D" by itself, holding down "option-D", holding down "command-option-D", reseting the SMC, and resetting the PRAM.

I'm at my wits end. I'd like to just assume that the current stick is good but the little voice in my head insists that it needs proper testing. Does anyone know what is going on?