1) IF the game as such runs and you have the mod installed properly (through installer or manually) and don't launch other mods along with it, then there is generally no reason why it should not work. Unless your new PC is crap..

2) DL for AGOT works fine for me on moddb.
Something (browser, addon, security, else) is likely blocking the popup, which you have to confirm to start the download. Clicking on the exe link in the first white windowmight help.