errrppp....for SP3 pretty much everything in \windows\system32 ought to be dated 14/04/2008 at 13:00:00 which is the 'standard' SP3 creation date. Looks as if something is pretty wrong with your SP3 install (mind you, mine is XP pro, but Home should be no different).
Hopefully someone else will tell us what date XP home SP3 should be???
Can you use windows search of system32 for all files on a specific date, creation date, including hidden files and folders, from 14/04/2008 to 14/04/2008 I get 3,643 files, and you should get something similar.
If not, you might try re-installing SP3 from a fresh download. I hesitate to recommend you do this if the PC seems fine, but supposing your system is actually still at SP1, you (a) will not be able to get security updates from MS, and (b) will be quite vulnerable. Only SP3 is still supported by MS.