I own a Dell XPS laptop bought 2004. It has a Pentium 4 CPU, not the Celeron.

Does or should it have an L2 cache memory? What size? How do I check if it is there or active?

I believe I may have disabled it somehow.

Some BIOSes have settings that will let you enable or disable the L2 cache.
Size for a Pentium 4 can vary from 256KB to 2MB depending on what type you have.
I don't believe there is any way to disable it except by doing so in the computer's BIOS. Check there to see if it is enabled or disabled.