Just installed last night on a Windows 7 machine, game was working alright except for intermittent lockups between missions and the screen randomly shaking persistently. Figured I would try the v1.10b patch, but now when running the game it asks me to buy the full copy or activate installation.
Any suggestions or ideas? I wouldn't mind reinstalling but I'd also like to prevent these other issues from reoccurring.

According to this, gog version is already pre patched to 1.10b.

GOG version is already patched to version 1.10d. You should generally avoid patching GOG versions as they are almost always patched to latest official version and they tend to restore any DRM/Copy protection present in retail version. There apparently is open beta for 1.11 but I've yet to find where you can actually download it.
Edit: Namur beat me to it :P

alright, thanks for the swift replies. i'll reinstall.
any ideas as to the shaking/flickering?

Long shot but try this.
Before starting the game, right click the desktop and choose 'Screen Resolution'. Leave that window open while playing the game.
It sounds ridiculous, i know, but you'll find quite a few reports here on the boards of problems with messed up colors and flickerings that are solved by doing just that, although for other games, thus the long shot.

The reason the 1.10b patch asks for a License is because Altar Games sold Original War on Sprocket, which use to use Softwrap (A DRM). GOG seemed to have taken Altars Digital Download copy but used the Retail EXE, since the Softwrap dll is present in GOG's version. The 1.10b patch looks for the presence of the softwrap dll (Which should only be in Altars Digital Download version) and extracts the protected EXE if its found.
Ultimately you can blame GOG for not contacting me, the guy whos been maintaining OW since 2005. Im not sure if GOG's version creates all the correct Registry Entries that it should (So things like the Master Server's "Host Game" link, or Join Game links work in browsers).
v1.11 Beta can be downloaded from OWSupport's (The Official Site for getting Support on Original War) Open Beta Test section of its forum(You have to register and join the Open Beta Test Group to see the forum).
The Win7 problems seem to be caused by Win7 as XP/Vista users havn't reported it. Have you tried installing Direct X 9.0c (Don't reply with "But i have Direct X 10/11" as they are separate to Direct X 9.0c. Installing DX9 will not do anything to the DX10/11 installation)?