Most DVD players are originally manufactured as 'region free' and can play DVDs from any region. The regional code is only added at the end of the manufacturing process and can be easily removed if you know how. (It's usually as simple as opening the DVD drawer and entering a 3 or 4 digit code via the remote control). If you search Google for 'DVD hacks', you might well be able to find the instructions to convert your an American (Region 1) DVD player to 'multi-region', so that you'll be able to watch UK (Region 2) DVDs with it.
That, of course, doesn't actually answer your question. The output from a PC or laptop can't be connected directly to a TV set but you can buy a converter for less than $40. There are plenty of suppliers in the USA. Here's just one:
http://sewelldirect.com/pc-to-tv.asp?&
Note that the converter advertised on that page connects to the TV via an S-video socket or via the RCA input. (That's the one using 'phono plugs'). If your TV only accepts a Scart cable, you'd either have to to get an adapter lead (to connect S-video or RCA to Scart) or seek out an alternative PC-to-TV converter with a Scart output.
Chris