There's a couple of possibilities that come immediately to mind. If you've been messing around with alternative shells jump to #2.
1. When you say you tried to start the explorer process I'm assuming from the Task Manager you clicked File / New Task, typed explorer.exe and clicked OK and then got the File Not Found error.
Try the same thing except this time manually browse to C:\Windows for it. If explorer.exe really is missing from C:\Windows then a stopgap solution would be to try to load the copy that is located in C:\Windows\system32\dllcache.
If both copies are missing I would seriously consider a reinstall because that should never happen and who knows what other files you're missing? If you do get Explorer running, open a command prompt and type SFC /SCANNOW to verify your system files. Also, do complete virus, adware and rootkit scans.
2. On to the Registry hacking. OBLIGATORY WARNING: If you've never used Regedit before, you can seriously bork your computer if you don't follow these steps exactly.
This assumes it was an alternative shell that caused the problem and you've gotten Explorer running now so click Start / Run, type in regedit and click OK.
This opens up the Registry Editor which is similar to Windows Explorer. Browse to HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Winlogon.
Find the value named "Shell". It is normally set to "explorer.exe" but if you've tried some alternative shells it will be set to something else. Right click on it, select Modify and change it back to explorer.exe.
Reboot.