If you're looking just for local admin privilege to run your applications on your current XP installation (instead of paying out for a Win7x32 Key), have you considered preparing a Bootable USB drive with Offline NT Password and Registry Editor
, re-enable the local administrator account and reset (or entirely remove) the administrator account password to get into it? It's worth a try anyway since it's entirely possible that it's only asking for local admin elevation to perform tasks with instead of network admin elevation. If it works, it would also be a good idea to take it out of the domain and put the laptop back into a local workgroup of your naming.
If the above fails and you still want to go over to Win7x32 then Ebay will be best to get your keys from nowadays. Just having a quick look, they're super cheap which is very handy, I can see x32 keys from around £6-£15 quite easily. Heads up though, most of the keys you'll probably find on ebay when you try and activate them will end up requiring telephone activation if the online activation fails from having the key installed too many times (some of the ebay key sellers like to sell the same keys multiple times over). Nowadays you can just go through the activation process as normal on your smartphone and then accept the option to activate it via code in a mobile browser as opposed to suffering through their crackly audio activation service haha.