Can only having one stick of RAM cause a kernel panic?

I was having spontaneous restarts and kernel panics with my late 2006 MacBook, so I took it into Apple for some testing. The logic board is fine, but I have a bad stick of RAM. We isolated and removed the bad stick, and I have a new set on the way from Crucial. Meanwhile with 1 GB of ram (in only one slot) I have still been having the same issues. Could these be caused by my lack of memory, or something much worse?