Ok, I finally got it.
Short version:
Avast! 4 evidently doesn’t like the Norton Protected Recycle Bin. Disabling NPRB solved my crash problem.
Long version:
After I said I had matters fixed in this http://forum.avast.com/index.php?topic=25746.0 thread, I discovered I hadn’t solved the real problem. I fixed the errors that were showing up in my logs, but Windows only successfully booted one time (after which I said I “fixed” the problem; ha!), then proceeded to regularly crash again.
I received a crash dump analysis from Vlk (thanks for putting in all the extra work!), and started investigating the problem. Doing a few boots under different conditions and with logs finally showed me that the crash occurred during the load of npdriver.sys, the driver for the Norton Protected Recycle Bin. I disabled Norton recycle bin protection, and whatdayaknow, Avast! works! (And yes, I have done multiple reboots this time to make sure it really works! 
)
For the record, I am using Norton System Works 2002 Pro on Windows 2000 Pro SP4. The version of NPDRIVER.SYS that caused the problem is 15.3.0.36, dated 2/5/2002.
Good luck to everyone, and thank you to those that helped get this worked out!
Jason