Hi HamSalad (assuming that's your real name! ):
You need to be running Inventory Solution 6.1.2004, along with the core Altiris Agent 6.0.2416. I see you have the R13 rollup installed, but I don't see mention of the Inventory Solution version. Assuming you're using the default configuration and have 6.1.2004 installed (you can check in Solution Center) you will probably want to remove the 16bit serial number gathering method. To do so, edit the AeXInvSolnAdm1.ini file and replace the AeXSNPlus line with the following:
aexsnplus.exe /NoSNData16 /output xml
Save the file and the next time the inventory runs (you can force the package to update, or just wait until the next day) you should see the Serial Number info reporting again. This disables the 16bit serial number extraction routines, which will fail on a 64bit OS.