This sounds familiar...You do have spyware and it was probably installed from a website you visited.
The one I dealt with had the same issue, where it would scan your computer and gives you a list of files that it says are spyware.
If you are getting that list, copy down the files and their locations. Those are the files that you need to remove.
I do not know if you have this particular file, but the program I dealt with had a file called 'sticky.dll' that is within the Windows directory. That is the file that is causing the icon to reappear even after uninstallation. Do a search for that file to see if you have it.
So what you need to do is to stop the program from running. Through a bit of luck, I was able to crash the program when I was removing it, but I forgot what steps I did to cause it.
I suggest doing the following:
Disconnect the ethernet cord if you are using one and make sure you disable your wireless adapter. You should not have any internet connection when doing the removal.
Restart the computer in Safe Mode. (Press F8 during boot up and you will get a menu)
Once safe mode loads, verify that the icon is not in the system tray. Now go to Add/Remove programs and unistall spylocked. Once that is done, do not restart the computer yet.
Using the list you copied down, manually delete the files listed that was not uninstalled. Restart the computer and it should be gone.
If on the off chance you are seeing the icon even in safe mode, you will have to crash it like I did. I think what I did was to uninstall the program after it has done it's scan while the infected list was up. Hopefully it will work for you too.
Just a note: The program I was removing was called spywarequake. It has similiar symptons to Spylocked. This was about a year ago. While the spyware might be different, I am thinking that the same steps should remove it. Give it a shot and see what happens.
A more simpler solution, might be to use System Restore to restore your computer to an earlier date, before you got hit with this thing, but that is not a guarantee it won't come back. There might be a file hiding in your My Documents folder.
Beware of websites you are not familiar with. A safer surfing technique is to disable Java and Flash when going to a new website. I use FireFox with No Script, this gives me the option to enable Java only when I feel it is safe.