This method worked for me on an XP operating system after attempting to uninstall 7-Zip and losing register mappings so that the only icons that still worked were My Computer and My Documents. I restored XP by opening My Computer, opening the Windows folder in my C: drive, then opening the system32 folder, followed by opening the Restore folder and double-clicking on the "rstrui" application file that starts the System Restore screens. If you wish to avoid any more work (provided you were able to Restore the system and it is working properly), skip to the aecond to last last paragraph for a quick and simple way to remove 7-zip as your default compression software without having to uninstall it. If you are disgusted with the "trial" version of 7-zip that refuses to be uninstalled safely, read on.
Once I restored the system, I used the "regedit" command from the Run screen in the Start Menu to bring up the register edit screen, then used the Find command to locate each instance where "7-zip" appears in the register and deleted each insatnce, whether a file, a path or a folder. Once all instances of 7-zip were deleted, I exported the register using the "export" command available from the "File" pulldown menu in the register screen. Closed the register screen then uninstalled 7-Zip by right clicking on the 7-zip icon on the desktop, selecting "Locate target file" and double-clicking the "uninstall" icon in the menu. Then opened the register again using regedit, and imported the register that had all 7-zip instances deleted. I got an error message indicating the import could not be accomplished, but tried importing once more, same error message. Decided to reboot the machine anyways and checked desktop item functions. They all worked properly and 7-zip was unintsalled successfully.
The final step was to bring up the Accessories->System Tools-> Command prompt and typed in the line "assoc .zip=CompressedFolder" command (without the quotes) to set the native Windows compression software as the default software to open .zip files and to allow choosing the Windows software to compress files.
This method worked on my PC, and may or may not work on other PCs running XP. If you can reach a Restore point, you do not necessarily need to uninstall 7-zip, you should be able to just enter the command line to make Windows your default decompression software. This should allow you to compress and decompress files with Windows software by choosing which software you wish to use.