My Nikon N-65 film camera seems to have died. Replaced the batteries and it will not turn on. During last year's NJ Challenge, the shutter froze while taking a photo. A camera shop managed to unstick the shutter, but I think it is dead.
I do have a nice 28-300mm lens for the camera.

So, I would like to buy a DSLR body that will accept the lens. Any suggestions or do you need more info?

If you go to the Nikon site it might tell you what lenses are compatible??
Not a likely senario. Latest and greatest auto focus and anti vibration probably will not be compatible with your lenses.
If your really are in love with the lens and film format you can look for a used or refurbised body.
Good luck!

Is the lens an auto-focus lens or strictly manual?

I used a Sigma 28-200 with my D-70 (bought it just before the 28 - 300 came out, of course). I used it as the only lens with the camera since it covered the range I felt I needed. Six years ago I changed over to the then new D-70, keeping the lens to use. Also have the kit lens that came with the camera. The lens is autofocus and works well with the D-70.

Remember that several of the new Nikon bodys won't accept the older style lenses (or, won't autofocus them). As I recall, has to do with the motor for the autofocus - on the newer cameras it has to be on the lens, since it is not in the body. I can use the lens from my daughter's D-40 but she can't use my lens unless she is willing to manual focus it.

Guessing Robert's lens is either a Sigma or Tamron autofocus, non-stabilized. Both are popular and reasonably priced lenses that worked well with the Nikon film bodies.

I have a Tamron AF lens. It is autofocus but I don't know about the motor. I guess I'll make inquiries at a camera store.