Long story short: if you're getting a Runtime Error 429 from MuleTradeIt!, and have already tried reinstalling it, try registering "MuleTradeIt!.dll" in the Mule Trade It program directory, as follows:
1) navigate in Windows Explorer to your MuleTradeIt! program directory ("C:\Program Files\GouruWare\Mule Trade It!" is default), and find the file "MuleTradeIt!.dll". Leave that window open.
2) go to Start Menu > Run, and type in "regsvr32" (without quotes). Leave the Run dialogue box open.
3) return to the Windows Explorer window, and left click + drag the "MuleTradeIt!.dll" file down to the Run dialogue box you just opened up, and release the mouse button. Your Run box should now read something like 'regsvr32 "C:\Program Files\GouruWare\Mule Trade It!\MuleTradeIt!.dll"'. Press OK, and you should see a dialogue box pop up informing you that the .dll was registered successfully.
4) The end.

Explanation: For some reason, the MuleTradeIt! MSI installer failed to properly call the registration of MuleTradeIt!.dll during the installation process. My extremely geeky "after-solution, re-troubleshooting" process ruled out 99.9% of all other possibilities that I'm aware of (details below for techies). Whatever causes this is beyond me, as it's evidently possible that it could be triggered by a single unavoidable and undetectable difference (such as an otherwise completely benign corruption occurring during a system essentials install) between three identical/110%-stable software/hardware configurations... yet it's not MSI's fault, which is almost a first in my 12 or so years as a programming hobbyist.

Re-troubleshooting details (reproducing the problem):
In a fit of curiosity, after the kids were in bed I took the liberty of completely reformatting mine and my son's drives and redownloading (ac/decal/plugins) + reinstalling everything from scratch, XP through AC through MuleTradeIt!, exactly the same as I'd done originally - to see if the problem would re-appear. It did show up again, and I fixed it the same as before - but guess what?
This time it happened on my machine, and my son's worked perfectly =) Talk about finnicky.
Good luck for those of you experiencing this problem.