Yes it is possible. I picked a Computer up for my son out of the local newspaper for £250.00. STS Midi tower, Creative 52x CD-ROM, Sony 32/10/40x CD-RRW, on board Modem 56.6, 20Gig hard drive, 17" Elonex monitor, Graphics Card and 2 USB ports and a HP Printer. I can't remember what the CPU was but I do know it was damn fast and the whole kit was only nine month's old and the kids father said he had only used it for about 10 hours. It was in mint condition. It may have been a one-off lucky find, but every week there are computers for sale in our local paper for around £200 to 350.00. Keep your eyes peeled in your local rag.
Our local Guru's repair shop sells second hand machines but only gives three months guarantee with them and they sell for around £400.00 to £800.00 each. My son's has been running for ten month's now and has never missed a beat. I know it can be hit and miss with these sort of things but at today's parts prices even if he had to pull a few quid out for something that did go wrong on it I think he has still got a cheap machine.