Is there a programme which can check memory

BritBrat

Take one stick of memory out and run computer if it still plays up swap out the one stick with the other.

If it's then OK I would say one of the memory modules is faulty.

As for testing use this:

Memtest86 you will need to run it for a few hours.

iviv

It doesn't sound like its a faulty stick, something is just hogging all the memory.
While in windows, hit ctrl+left shift+ escape to bring up the process manager. One of the columns should be 'Mem usage'. If not, go to view> Select columns and make sure memory usage is checked. Sort by memory usage, and look at the programs that are using alot of memory. If you don't have anything open on your computer, then anything abouve 50,000K will be suspicious. On my laptop, Firefox with a couple of tabs open is around 50,000K.
If you are using Vista, there may be some things with more than 50,000K. Still, if you could list them, it would help.

The most lkely problem is spyware/malware thats clogging the computer up.
Spybot S&D, Adaware and Windows Defender are all good programs to run.