The trial version is the complete version - it just needs to be licensed with a key.
You'll need to call Adobe to see if they would provide you with a key for LR4, since it isn't a current version.
LR 4 is obsolete as far as Adobe is concerned. They will not sell a Serial Number for it. The Serial Number for LR5 will not work with it, as they are version specific.
Your best course of action, is to get in touch with "Customer Services"
gvb279, the Adobe site is so twisted, that it does not give an email ID for Customer Services or support. Whenever I click on the 'Still need help Contact us' button, it takes me to the 'Need help? Start here to get support''. Check out the link.. Contact Customer Care
Would you have the Adobe Customer Services Email ID?
There are still retail packs of LR 4 to be found out there - for example, on EBay. It's just important to be careful whether it's a full version, an upgrade, or a student + teacher version. And to be certain it's genuine, and has a serial number which has never been activated before. The serial number that you get with that, should work with any 4.x version of LR, on either MacOS or Windows. And it will almost certainly be heavily discounted compared with the previous price direct from Adobe.
Of course the other way is to upgrade to Windows 7 SP1, which should also be available discounted, and thus eke out the life of an older PC (I personally would not go to Win8 in such a case). Maybe pick up some RAM also, if that's a problem, provided you can do so cheaply (since that will be simply thrown away in due course, when you get a newer PC),
Using LR4 instead of LR5 you do miss out on a few nice features, as well as potentially the Raw support and lens profiles for more recent camera equipment.
LR 4 is obsolete as far as Adobe is concerned. They will not sell a Serial Number for it.