Will lenses fit Nikon DSLR Camera?

I had a (non digital) Nikon SLR camera with a standard lens and a zoom lens. The camera no longer works, but there's nothing wrong with the lenses.
If I buy a Nikon DSLR will these lenses fit it, or is the DSLR lens something different?

Yes they'll fit but won't autofocus on some cameras, notably the D40, D40x, D60, D3000 and D5000.

They work fine on the D50, D70, D80 and D90 (and higher end cameras) provided that the lens is AF in the first place.

Yes, they will fit. If they are AFS or AFI lenses they will auto focus on all Nikon DSLR's. If not they will fit but will need to be manually focused on the entry level models.

It's a list as long as your arm!

AF-S/AF-I, motorised Tamron, Sigma and Tokina lenses- fit all current Nikon DSLRs will autofocus and autoexpose on them.

AF/AF-D, non-motorised Tamron, Sigma, and Tokina lenses - fit on all current Nikon DSLRs. Will autoexpose on all of them. D40/40x, D60, D3000, D3100, D5000 won't autofocus.

Carl Zeiss ZF/ZF2 - fit on all current Nikon DSLRs. Autoexposure on all of them. Carl Zeiss lenses do not support autofocus.

AI/AI-S, other AI standard third party lenses (e.g. Vivitar lenses) - fit on all current Nikon DSLRs. Autoexposure only on D200/300/300s/700, D1/2/3 series cameras as well as Fujifilm S5pro. Other cameras will not meter.

Pre AI lenses - need to be converted to AI standard to be compatible with DSLRs.

Yes, you can mount any AI or later lens on your DSLR Nikon. Will it work? No.
If you have a D1, D2, D3 or D700 it will meter just fine. These pro line cameras were built to work with almost all of the Nikkor leses made. While they will not auto-focus, the focus indicator in the viewfinder works very well as long as the lens is f5.6 or faster.
For almost all other Nikon DSLR cameras (all of the consumer models) the meter does not work and the focus indicator will not work either. I've tried manual focus AI lenses on these camera bodies and the results were poor. Even with a hand held meter to set the exposure the results were iffy. Basically, if the camera does not have a depth of field pre-view button, you can't use these lenses. Even the D100 will not meter with AI lenses.
See if you can borrow an old AI lens and try it out.