This post isn't written simply based upon a bit of googling. I also use Windows XP and (like 85% of XP users) I'm in no great hurry to upgrade my operating system.
Windows XP doesn't support the latest versions of Internet Explorer, so you're forced to use an old version, which Microsoft is no longer providing security updates for, So I'd definitely advise against using Internet Explorer on your computer. (OK, let's be honest here. I'd strongly advise against using Internet Explorer on
any computer. It's total c-r-a-p!!!).
I've no idea why Chrome won't run on your computer but I could never get on with it anyway. (I know that it's got lots of fans but it's simply not for me). My favourite browser (and from posting on thousands of threads here in 'Technology', what appears to be used by the vast majority of AB members) is the wonderful Firefox:
https://www.mozilla.org/en-GB/firefox/new/
So why not give it a try?