It's perfectly normal for the wine cork to be wet if the wine has been stored on it's side and it doesn't always mean the wine has gone bad.
However sometimes the wine may be bad if the wine cork is wet but the taste will be off and the wine will smell bad if the wine has gone bad enough to be thrown out.
I've drank wine before that had the wine cork wet and it was okay to drink and I never got sick.
After you do open the wine be sure to refrigerate it and drink the opened bottle of wine within 7 days because after 7 days the wine will go bad.
If you think the wine is bad enough then you should throw it out but tasting the wine and smelling it can be a good way to tell if the wine is good or bad.
Having the wine cork be wet is sometimes an indicator of bad wine but not always.