The second one couldn't be mounted be neither Linux nor Windows, as Linux kept reporting various seriously-looking NTFS errors. On the topic of NTFS, it seems really ancient, closed, unportable and inefficient. We're in 2013 and it still has those awful fragmentation problems?! No permission?! What a joke of a filesystem...
Anyway, due to not having an external HDD container, I had to open up my PC and connect his HDD to it. While booting, Linux reported some errors about it, which was a bit strange. I can't remember what they were, as I forgot to write them down.
Anyway, once I was up and running, my PC could read the first, uncorrupted partition, as I had expected. However, there was no sign of the second one.
Well, if you have such a problem - or any other problem with your HDD (as long as the data itself isn't heavily damaged) - there's a solution!
The solution is called Testdisk. It's a free and open source data recovery tool (CLI) developed by CGSecurity.
apt-get install testdiskshould do the trick.
When you've installed Testdisk, run it by giving it root permissions (sudo testdisk, e.g.). I chose "no log" as the logging option, as I didn't really need one. After that, select the correct media and the partition table type (you should probably go with the default selection (Intel)). After that, you're presented with a menu. You should go under the "Advanced" tab, after you've ran the analysis (default selection), as it offers you a way to navigate through files.
Once you're in the advanced tab, you should see a listing of your partitions. Select the one you're interested in, and go with the "List" option.
And, voila, all your files are right there (hopefully)! You can select the most important ones, and copy them to a desired location.
I hope that this short tutorial helped you.