I turned an old Thinkpad 600e into a photo frame a couple of years ago. Biggest expense was getting a nice wooden frame to mount everything in, so it looked nice.
Took the surround off the screen and laid it on the back of the laptop, facing out. Used FreeDOS as the operating system, plus a simple slideshow app I found online. Have to resize the photos to match the screensize (using Picasa) and upload files manually, but it works a treat.
Things I love ...
... Even though the display is only 256 colours, it's good enough. I've had colleagues at work think the photos are real, until they work out the picture is different every time they look at it.
... It makes use of the photos. Instead of the photos being locked away in a folder and seldom, if ever, viewed, the photos on the frame get seen.
Things I'd do differently ...
... Without USB support, the only way to copy photos on is via rewritable CD. A bit of a PITA - having it on the network (wired would do, wireless would be better) would be much easier.
... I'm worried about the hard drive possibly not spinning up next time it gets power cycled. Having something flash based to store the photos together with an OS that does good power management and turns off the hard drive when not in use would last longer (and use less power and be quieter).
So, I'd suggest you find yourself an outdated (and therefore cheap) laptop that still works.
I'd look for one running Windows XP(*) as you get all the good application and hardware support, and there are lots of old laptops that will run it just fine. Set up a DropBox account or something similar, put it on the network and forget about it. Drop the photos you want to display into the dropbox and watch them come up on the screen. Use a photo based screensaver to show the photos - Picasa has one, but there are others.
(*) Yes, Linux would work just fine - but I don't have the skills to make that work without spending too many hours learning new stuff. YMMV.