Problems with two brand new TBOs in a row, that must be very frustrating. :(
I've not experienced this exact issue, though one vaguely similar. If I try to connect a Microsoft Comfort Optical Mouse 3000 while my Trackball Optical is connected, the TBO will function erratically (buttons work intermittently, the cursor occasionally moves in only one direction, the scrolling wheel won't scroll up). To correct the issue, I unhook the Comfort Optical Mouse and restart my computer. I suspect that the malfunction I've seen is caused by a conflict when the two similar devices interface with the IntelliPoint drivers and software.
For your situation, the only advice I can add is:
-Make sure your Trackball is the only pointing device connected to your computer
-Connect it via USB directly (no hubs, converters or extenders)
-Verify that another pointing device will work properly when connected through the same USB port
-Check that the translucent plastic ball socket is clean and the optical sensor unobstructed
As you've tried the TBO on clean installs of both XP and 2000, I doubt software, drivers or operating system are the problem. If none of the sugestions above or from others help, the TBO itself is likely defective... A damaged LED, sensor, USB cord, solder connection or PCB defect - it's hard to say. Since you purchased it new, I'd return it and either get a refund or have the seller send another and hope the 'third time's a charm.'
If nothing pans out and you're interested in buying one new from a different source, there's a guy on ebay selling new, boxed TBOs for $155 USD via 'Buy It Now' with a 90 day warranty. It seems that, if desired, he'll open the box and make sure it works before shipping.
Link to the auction. (I've no affiliation with the ebay seller - or ebay :) - I just happened to stumble upon the auction earlier today)
Best of luck to you. My apologies for not being able to assist further.
-Z