Freezing Windows when stray pixels appear

On new Dell Dimension W98 on last two days there has been an intermittent problem lasting 2-3 hours each time when the system completely freezes - the keyboard is no use, but the mouse moves around the screen although clicking anywhere does not help. I have noticed that this problem occurs after a boot (or reboot) when for some odd reason some stray pixels start to appear around the cursor.  I have tried uninstalling/reinstalling both peripherals and software in the hope of isolating the cause but to no avail.  Also, the hard disk churns away pretty much non-stop for about 1o munites before returning to normal.  The odd thing is that sometimes when I boot up the system works perfectly (like at present).  It is only when the stray pixels appear around the cursor (sometimes it is just one dot but at other times it is 5 - 10) that I know I am just about to hit trouble.  I have talked at length to the Dell support but they have so far been unable to help...  I am of the feeling that it is something to do with either Windows Media Player or a driver that controls the monitor.  What happens is that the boot-up proceedure runs normally, and then at the very last point before the end of the boot-up, the pixels appear by the cursor.  Then after a couple of minutes of working on the system (it happens when surfing, using Excel, Word, fax utility, scan utility etc, - in fact this does not seem to be  application-specific, the system freezes - always when there is 'movement' on the screen i.e. a web page refreshes, or even when opening a windows box like the system config box and you grab the window to move it across the monitor.  Sometimes large white patches appear on the monitor, sometimes a strip of black/speckled area appears across the screen.  The system is only 10 days old.