Thanks for Your reply. I managed to deal with the problem. All it took was taking out the card and putting it in again. There must have been an issue with the connection somewhere. The sound problems are gone, my PC starts up perfectly and the performance is satisfying.
After taking the card out I noticed, that two of the connector pins (I don't know how they're correctly callled. I'm referring to these tiny, rectangular copper plates located on the part of the GPU, that is inserted into the slot) are significantly (about 1/4 of lenght) shorter than the others. Is that bad? Are they broken? There doesn't seem to be any damage in the vicinity, and the copper plates are perfectly cut.