I know it may sound like an odd question, but it's the only PC I have and I'm wondering if it can run Morrowind or not.

But not just Morrowind, Morrowind with some mods and texture replacers.

here are the system specs:

Model: NV51B
Processor: AMD C-50 Processor 1.00 GHz
Installed Memory (RAM) 3.00 GB
System Type: 64-bit OS win 7
Video Card: AMD Radeon HD 6250 Graphics

I would say it would be OK. I ran Morrowind with mods for bodies and faces, on a netbook with a Intel Atom N270 processor and 2 gigs of memory. Played the whole thing and Tribunal with no trouble.

I believe it can but not with any huge hi res texture replacers or anything. Then again I am no expert.

I would think that 3 gigs of ram would suffice but I don't know how good (or awful) that gpu is.