With more info on the system it's hard to pin this down to one thing....You could be running short on RAM on the slowness issue.....give a program like Free RAM XP a try for that
http://www.yourwaresolutions.com/products.html
...Try manually closing all the programs running before trying to close down and see if that helps....and give the old three fingered salute (ie press CTRL + ALT + DELETE) which will bring up task manager and will let you see whats happening......if all else fails try googling for "windows hang on shutdown" and see if any of the info is applicable.