Numerous Trojan warnings since last update.

[Ugamark]

Tarq57,

Thank you for the response.  On second glance, you are correct on your assumptions.  First, these were the entries (times 19-20) from the IOBit software file false-positive:

12/2/2009   8:21:18 PM   1259814078   SYSTEM   1736   Sign of "Win32:Delf-MZG [Trj]" has been found in "C:\Program Files\IObit\IObit Security 360\is360mon.dll" file. 
12/2/2009   8:21:22 PM   1259814082   Mark   6980   Function setifaceUpdatePackages() has failed. Return code is 0x2000000A, dwRes is 2000000A.

But it also flagged a few items in my Google Chrome cache, and then some random error entries, which I am not sure whether they are part of the problem.  For example:

12/2/2009   7:17:44 PM   1259810264   SYSTEM   1736   AAVM - scanning warning: x_AavmCheckFileDirectEx [UNI]: C:\Users\Mark\AppData\Roaming\Microsoft\Office\Recent\JW Outlines.LNK (C:\Users\Mark\AppData\Roaming\Microsoft\Office\Recent\JW Outlines.LNK) returning error, 00000026. 

Nothing was quarantined, so I have nothing to restore.

I do have several antispyware/malware programs on my computer (But Avast is my only antiVIRUS program), including Spyware Terminator, which now no longer runs at startup as a result of the Avast false-positive.

And you are correct--the restore was successful, but it did not fix anything and my computer runs no better.  My computer freezes when any Windows-generated prompt must come up (i.e., deleting a file, it freezes when the O/S would normally confirm the deletion).

[Tarq57]

How I'd try and proceed would first be to try and get the database updated. Try pausing all the providers, and/or selecting "stop on access protection." If it is stopped, it may, relieved of its load, be possible to update it. Once updated, start everything up again.
If no luck there,attempt a repair of Avast via the control panel programs application.
Locate the entry for Avast, select "change" then "repair". Normally takes about a minute. Once that is done, see if it can be updated.

I think what may be happening is that Avast still thinks the files it flagged are malware, and is preventing any such file running, even though the "no action" response has been made.(And maybe in so doing it is consuming all your resources, thus freezing on attempting to open the GUI.) So trying to get the latest (or at least, not the corrupt) database is probably the most important thing to do.
Once that is done hopefully things will improve, radically. (It's guesswork on my part, tell the truth. Semi-educated guesswork. But it makes sense.)

If Avast can not be repaired, it may be necessary to remove it completely, use a special tool, and re-install. (Instructions late, if required.)

Let me know how the repair goes, first.

[Ugamark]

Tarq--Your advice was brilliant.  PROBLEM SOLVED!!!  For reference, to anyone who encounters similar problems, I did a "Stop Provider" of all Avast protection (from the right-click menu of the task tray icon), then restarted the computer (at which time, all missing startup programs returned), updated Avast, and then re-updated Vista (because I had reverted my o/s to an earlier restore point).  THANK YOU so much for your expertise.

[Tarq57]

You are very welcome. Really glad it achieved a good fix. 
Wish it was as straightforward for all affected users!

Now you need to check you quarantine, re-scan any file that may have found its way there during the problem period, if it re-scans clean, restore it. If for any reason it fails to restore, try extracting it too the original location.
Just a bit of housekeeping. Hopefully nothing further will be needed.
Any problems with any program, it's likely re-installing the program will fix it.