Chances are that System Restore does NOT need reinstalling - just switching
back on

Firs thing to check is that you have the correct startup programs
Go to Start | Run
type

MSCONFIG

click OK
You'll get a window pop up, with a number of tabs - click on the Startup tab
in the list there, make sure that there';s an entry for "*Statemgr" (without
the quotes), and that that entry is ticked.
click OK, but refuse the offer to reboot for the moment

Go to Start|Search
in the 'Find files named...' box type "smgr.dll" and click OK
you should find a copy of the file in the C:\Windows\System folder - r-click
on it, and select Properties, and click on the Version tab of the box that
comes up. What version is declared there? - close the window

Now open Windows Explorer (or My Computer - same thing)
In the toolbar at the top, click on Tools, then Folder Options, and when the
window comes up, click on the View tab.
Under the 'Hidden files and folders' heading, check the 'Show hidden files
and folders' radio button. Just below that UNtick the 'Hide protected
operating system files' checkbox. Click on OK to return to Windows Explorer.
Now navigate to the C: drive, and open that so that you can see the
contents. The first folder in the C: drive is usually _RESTORE - right click
on that folder icon, and select Properties. You can see there, the amount of
space that SR is currently using, and the number of files it's got. The
number of folders *should* be 5 - if it's anything else, then you have a
problem!

reboot, and see whether System Restore works now - post back with the EXACT
error message if not, and the results of the above actions

HTH

It is unlikely that you need to reinstall" system restore although you may
need to reset its control files.  What is the exact problem you are having
including the text of all error messages. It might help if you were to
perform the following quick text and report on all/any errors encountered.
a) Create a shortcut on your desktop to a file.
b) Create a manual checkpoint
c) Delete the shortcut
d) Restore you PC to the checkpoint you created.
Was the shortcut restored?  Did you see any error messages?