You might start here:

Troubleshooting Windows 98 Startup Problems
http://support.microsoft.com/?kbid=188867

If this doesn't help and you have sufficient disk space try installing to a
new folder as described in this article:

How to Install Windows 98 Into a New Folder
http://support.microsoft.com/?kbid=193902

Then install your anti-virus and scan the system.  If you don't have a
current anti-virus program, you can get one free from Http://www.grisoft.com 
The above article also gives you instructions to get back to your original
installation if desired after the install to a new folder.

PattyL

Try the procedures here:
Blank Desktop or Illegal Operations Error Message After You Install Internet
Explorer:
http://support.microsoft.com/?id=kb;en-us;249191

If those procedures do not help, have a look here:
Recovering From a Failed Internet Explorer Upgrade in Windows 98:
http://www.cs.bsu.edu/~gjjones/administrivia/stories/2003/03/21/recoveringFromAF
ailedInternetExplorerUpgradeInWindows98.html
or
http://tinyurl.com/r5ba

Especially this section at the end:

"If you still have boot problems after you reboot, you should use the command prompt
to edit the c:\windows\system.ini file. On the command line type edit
c:\windows\system.ini.

"Once it is open, change the line shell=explorer.exe to shell=progman.exe. What you
are doing here is changing the default shell (that is having problems) from the
Windows Explorer to the old Windows Program Manager shell.

"Reboot Windows. It should now successfully boot with no errors into an empty
Program Manager shell. Use the File | Run | Browse drop down menu selection to
browse to c:\program files\internet explorer and launch ie5setup.exe or ie6setup.exe
(depending on what is there). Do a custom install and check all the Bold faced
options. When the setup program alerts you that these files are already installed,
tell it to reinstall all of the files.

"When the Internet Explorer Setup program is done and reboots, hit the F8 key to
bring up a Boot Menu. Choose Command Prompt and boot to the command prompt. Once
there, type edit c:\windows\system.ini and, once it is open, change the line
shell=progman.exe back to shell=explorer.exe. Save and exit the file. You have now
set the shell back to the original value."

This will not solve the cause, but it may get you a desktop with icons if all
of your files are still in existence and in the right place.  And it will be a
starting point.   -- For win98 SE, cut the following (including quote marks):

"C:\win98rel1\Application Data\Microsoft\Internet Explorer\Quick launch\Show Desktop.scf"

Press Winkey+R.  

Paste the above cut (OR type it) into the Run box.  (Looks like a mess to type,
I cut it from my run window.

Press enter.

Voila?

.....OR......

You may get by just by hitting the WINKEY (usually between CTRL and Alt
on the left) and using the START lists....assuming that comes up as normally
is the case.

....OF COURSE.....

There are about a gazillion reasons this could be happening...view desktop
as web page, hide icons, hide toolbar, etc.  And some malware may have
made those settings for you and it may be a matter of undoing the settings
and removing malware, spyware, etc. from your machine after that.  
Check MSCONFIG and see if anything funky is running.  IF you do get it up,
it will probably best not to shut it down until you have to OR you are satisfied
that the problem is fixed.

FACE(Outgoing wordwrap turned off for this message.)