XP with SP3 memory issue

For some time now I have noticed that several applications will not shutdown properly and will other use up memory very quickly. Also some applications will not start if an existing copy is running.
I am getting this with several well known applications. Outlook, Winword, Powerpoint, Corel paint shop pro X2, Firefox (although the latest version downloaded seems to have fixed it for Firefox).
I can easily stop them by using taskmaster to kill the processes, but I should not need to do this.
This was very insidious, and I cannot be sure when it started, but recent downloads may be a factor. I am running XP Pro, SP3, Microsoft Office 2003 fully up to date.
I have recently downloaded/installed Logmein Pro, and installed Norton 360. I am a very experienced Windows user, but this one has got me beat.

Any suggestions please?

(BTW I always virus scan, remove adware and other spybots, and have active protection on all the time. I do not think it is a virus, but these things are never certain.