..where do these end up, how do I see if my computer "had one"? Seemed like it did SOMETHING last night....

A program core file is written in that programs current working directory. The best way to find them all is to "find / -name core -print". You can also use locate if the data base has been updated since the program dumped.

/dev/core
/proc/sys/net/core
/usr/src/linux-2.4.7-10/net/core

..is what I got. None of these are giant bomb files...so can I assume I don't have one? Are these files a place for core dumps to go, or somehting else?

/dev/core is a symbolic link to /proc/kcore which is read-only access to physical memory.

/proc/sys/net/core is a directory. Not real sure whats there but intution would lead me to believe it has something to do with the running state of the next item.

/usr/src/linux.../net/core is a directory containing the source for "core" functions for the "net" protocols.

You're right. None of these are core dumps. To avoid finding these in the future, restrict the find to files only. "find / -type f -name core -print". I should have done that the first time. My bad...