Norton does pop up saying it has found a trojan/virus called downloader and says it has deleted them.
What was the name of this Trojan? Did Norton provide a specific file name associated with it and a location?
Try running the the System File Checker
(SFC) to scan all protected files to verify their versions. If SFC discovers that a critical system file has been damaged, altered or missing, it restores the correct version of the file from the cache folder. You must be logged on as an administrator or as a member of the Administrators group to run sfc and it may ask you to insert your XP Installation CD so have it available.
Use Task Manager > New Task... and type: sfc /scannow
Make sure that you include a space between the c and /. This command will initiate the Windows File Protection service to scan all protected files, verify their integrity, and replace any problem files.