Does anyone no of a cheap digital camera that lets you control the shutter speed?

Well that feature does not come with most cheap digital cameras.

I have a nikon d40. It works great and I can make the shutter speed about 32 sec.

I bought mine refurbished on ebay for about $300. That is without a lens. I paid $60 for my lens.

I hope that helped

NIKONUSA.com

I don't know about "cheap", but there are "cheap-ish" cameras that allows shutter speed control. The Canon Powershot A-series has full manual control. Also, the Canon Powershot SD series allows you to manually set long shutter speeds (but not short ones).

That depends entirely on your definition of cheap. My namesake below had a good idea on where to buy one.

Look for used DSLR's from Canon or Nikon. You should be able to find one in the $300 range.