Is anything else missing or odd about your desktop? Whenever you have an unexplained Group Policy restriction, malware is usually at the bottom of it.
Download, install, update, and run (not at the same time) scans with these two free tools:
MalwareBytes AntiMalware
SUPERAntiSpyware
Can you put My Computer on the Start Menu (rather than an icon on the Desktop)? --> Right-click Start > Properties > Start Menu > Customize > Advanced > check appropriate box in the list > OK
Can you see My Computer in a Windows Explorer window?
Because you have XP Pro, the Group Policy editor should be available to you (if it, too, hasn't been disabled by malware).
Start > Run > gpedit.msc > OK
There are several places to check:
User Configuration > Administrative Templates > Desktop ---> if "Remove My Computer icon on the desktop" is Enabled, disable it. (If this policy is enabled, you wouldn't be able to see My Computer on the Start Menu or in Windows Explorer, in addition to it
not being on the Desktop).
User Configuration > Administrative Templates > Control Panel > Display ---> If "Hide Desktop tab" is Enabled, disable it.