Thanks for the replies!
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Is your reinstall of XP really fresh?
I did reformat my hard drive (using the "quick format" option) before I installed the OS.
It turns out I was typing the wrong serial number after all. I write down my serial number on every AM disk I get so I don't forget it. On the past two disks (two years), I left out a number, so the serial was only 6 numbers long instead of seven. When I checked some disks from three or four years ago, the correct number was on them.
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Did you check the AM site for system requirements? Like some software you need to have installed (DirectX or ???)?
After successfully installing AM, a cryptic program window popped up that was apparently trying to connect to the Hash ftp site, but the folder structure on the ftp sit had changed, so the window just displayed a 404 error. It turns out this window was trying to tell me I needed some important files that were in the v14Stuff.exe file. (which is on the Hash ftp site, if you can find it). After I installed the "v14Stuff", everything works great.