I'm in a bit of a pickle here. I managed to copy the whole postgresql installation directory to a backup drive but how would I retrieve it from Linux with the same architecture and version. Is this possible? I wasn't able to do a backup.
There's no way to dump your Windows PostgreSQL database directory using Linux directly1.
You need to start up a virtual machine running Windows, then copy the database directory to that virtual machine. You can then
pg_dump -Fc it, and
pg_restore the dump to your new blank PostgreSQL install on the Linux machine.
You must make sure that if your PostgreSQL data directory was from 64-bit PostgreSQL you install a 64-bit Windows version and install 64-bit PostgreSQL on it.
If your PostgreSQL data dir is 32-bit it doesn't matter whether you install 32-bit or 64-bit Windows, but you must install 32-bit PostgreSQL.
Licensing restrictions mean that you can't just download a virtual machine image for Vagrant or whatever to run Windows. You will need a Windows install DVD or ISO image. It's possible to download these legally from Microsoft's digital distribution system if you don't already have a DVD or ISO. You can install them without a license key, but it'll disable its self after a few days, and it's not legal to use it without possessing a license.
For that reason, unless the database is really huge one of the best options is to sign up to Amazon EC2 (if you haven't already) and launch a Windows Server virtual machine on EC2. You can install PostgreSQL then copy your database to that virtual machine, run
pg_dump, and copy the dump back to your computer. Then just shut down the VM. You can use EC2 for free if you use a micro instance.
1 It's possible you might be able to run PostgreSQL using WINE, but I suspect that'd be even more complicated, if it works at all, and probably not particularly trustworthy. So just use Windows.