Installing SP3: "internal Error", But Can't Repair Product Id

I have XP with service pack 2 already installed. I tried installing sp3, following all the guidelines about being an administrator, closing all programs, disabling virus scanners and such, but consistently get this "internal error" as soon as the installation starts. The event viewer doesn't say anything useful, but according to http://support.microsoft.com/kb/949384/ this is a problem with a funky product id.

The solution says I should go to the System Properties to get the product id. Well an abstraction of that product id is 69831-xxx-xxxxxxx-xxxxx. Then it tells me to go to HKEY_LOCAL_MACHINESYSTEMWPAKey-XXXXXXXXXXXXXXXXXXXXX, and work with the fields in there. It predicts that there might be more than one key conforming to that format, and there is. It says I should pick the key that has the same ProductID as found in the System Properties, but they both have the same id and it isn't what I found in System Properties, it's 55285-xxx-xxxxxxx-xxxxx.I have one product id in System Properties, and another that appears in two keys in the registry.

Here's my SysInfo:
Tech Support Guy System Info Utility version 1.0.0.1
OS Version: Microsoft Windows XP Home Edition, Service Pack 2, 32 bit
Processor: AMD Athlon(tm) XP 2600+, x86 Family 6 Model 10 Stepping 0
Processor Count: 1
RAM: 1023 Mb
Graphics Card: NVIDIA GeForce 6200 , 128 Mb
Hard Drives: C: Total - 103936 MB, Free - 25331 MB; D: Total - 13228 MB, Free - 8921 MB; G: Total - 70605 MB, Free - 11730 MB;
Motherboard: Gigabyte Technology Co., Ltd., nVidia-nForce2, 1.x,
Antivirus: AVG Anti-Virus Free, Updated: Yes, On-Demand Scanner: Enabled