Celeron 2.8ghz vs. Core2Duo 2.26ghz... is there that big a difference?

I think you've answered your own question. If a laptop is faster than your home pc and it includes the parts you want to upgrade to, then yes it will be faster. The Core2 series is a step up from Celeron, it has a bigger cache (celeron might not even have a L3 cache, which core2 does), and you will see a speed difference. You might also want to reinstall XP as I've heard of users having to reinstall it every so often to get it up to speed.