The first thing I would do is to work on restoring your missing system files
and then work on getting System Restore functioning correctly. Most of your
system files (VXDs, DLLs, EXEs, etc.) can be restored straight from the hard
drive (however, I strongly suggest updating any hardware drivers from the
manufacturer instead of the hard drive).

When WinME is installed, there is a virtual copy of the OS made in:
C:\Windows\Options\ and its subfolders.

You may restore individual files using this method:

START->

RUN->

type MSCONFIG->

select EXTRACT FILE->

type the file's EXACT name that is to be restored (not the complete path,
just the file name including extension, such as EXPLORER.EXE)->

select the "Restore From" location (in almost all cases, it is
C:\Windows\Options\Cabs\)->

Select the "Save File In" location. This is the complete path (the original
folder) where the missing file resided. (If unsure, consult Google using the
missing file's name)->

If you are replacing an existing file with this method (such as when
repairing a corrupted file), instead of restoring a missing file, you will be
prompted to create a backup. Always select "Yes" to be on the safe side.

To answer your second question, you may try to burn the entire folder:
C:\Windows\Options\ onto a disk for safe keeping (or for restoring files from
command prompt when normal and safe-mode boots fail) but the above (MSCONFIG)
method will work as long as you are at least able to get into safe-mode.

Only after your system files are restored would I worry about fixing System
Restore. Without these missing system files, System Restore is virtually
worthless anyways.

I hope this helps.

~Theta Sigma