Alright mate, basically the demo was only available through steam before the game was released. After that there was no more demo and I don't think you can play one to this day.
Best bet is to borrow a friends account to try it, or maybe watch some youtube vids of it being played in game to get the feel for it.
My PC is at least 2 years old now and it runs LFD fine, the beauty part of it is that it is the SOURCE engine. So if you can run CSS, HL2 and TF2 reasonably, you can play LFD.
I run it on a Geforce 8800 GTS and it's absolutley fine! You can find it cheaper if you buy the disk online ~£20 instead of closer to £30 through steam
I highly recomend this game though, it's such a good crac when you're playing with the OcUK guys.
If this is a bit much to stretch too then you should investigate QuakeLive for a good (FREE) fps game:
http://forums.overclockers.co.uk/showthread.php?t=17982275