Lost Product Key

If the game is still installed, the product key should be in your registry. Press windows logo + R on your keyboard, type regedit and hit enter. Then Mass Effect 2 should be located in HKEY_LOCAL_MACHINE\SOFTWARE\BioWare\Mass Effect 2. (I tested this myself and didn't find it, but maybe you're lucky.) The key should be located there somewhere.

Edit: It could be under HKEY_CURRENT_USER instead of local machine, but I don't see it there either.

I found a few things under SOFTWARE/ElectronicArts, but there are no game names, just codes. It could posablely be one of those, I just did not want to take the chance to get it wrong.

Thanks for the answer.

I now realize I'm making it harder than it should be. If the game is installed, the key can be found in the configuration utility. (Binaries folder in the installation folder) Click on the 'Game' tab.

Having found my key, I have found the location in the registry. Not that it matters, but here it is: HKEY_CURRENT_USER\Software\Electronic Arts\EA Core\Staging\eadm\eadm\online_content\mass_effect_2\ergc