Normally this problem of disappearing of desktop icons caused by the virus called called F-Nimda which creates a file named bxomebc.exe which aborts the windows explorer from starting. But this problem could be due to the corrupted registry also.
First download the
F-Nimda virus removal tool. and run it.
if the nimda removal tool doesn't work...try this if you're comfortable editing the windows registry:
WARNING!!! Editing the Windows Registry can hose a windows installation if done incorrectly!!!
After you log on to your computer and your icons/taskbar disappear do Ctr + Alt + Del to open Windows Task Manager. In Windows Task Manager click File, New Task and when prompted type regedit.exe .
Regedit will open. Go to the folder that says HKEY_LOCAL_MACHINE, Software, Microsoft, Windows NT, Current Version, Winlogon
click on Winlogon only once, do not expand it.
Locate Shell on the right hand side. Right click on Shell and change its value to explorer.exe if it isn't already.