So I installed Windows 7 on my PC first, then Linux Mint 17.2 Cinnamon onto the same hard drive. Then I installed the LAN driver under Windows 7 because it didnt't recognize the interface at first. After the reboot the internet connection under Mint was gone. I can neither ping some webserver, nor the gateway in the network, but it's still working perfectly fine under Windows. I think this is quite strange, because what I'm doing on one OS should not affect the other one, right? Pinging anything just returns "destination host unreachable".
Also the problem can not be Windows not releasing the IP address because I'm using static addresses. The network I'm working in does not provide DHCP.