Most Efficient Way to tune rear gears of mountain bike
Generally, if you haven't bent the derailleur (or its hanger) [such as by having a crash], you should have been using the barrel adjuster as shown in this image 

 

(from here)

in order to make tweaks to the adjustments. The mis-adjustment you were experiencing was likely just "cable stretch" in the non-bent case. The barrel adjuster changes the cable tension, which you were more drastically doing by undoing the bolt which holds the cable (so you may have put wrong cable tension now). From the description, it sounds like you don't have cable tension (and thus the shifters can't pull anything and shift).

The rest of the adjustment options (screws) change the derailleur limits (big and small cog) and angle of the derailleur (b-tension). These should be set-it-and-forget-it (unless the derailleur gets banged up, in which case it must be un-banged up and then possibly re-adjusted). 

Park Tool has a good description on how to adjust a derailleur, which you should read and implement (or take the bike to your LBS, give the guy 5 bucks and get him to adjust your derailleur and check if its bent). If the derailleur/hanger is bent, it must be un-bent prior to adjustment. 

Another thing that may be occurring (though unlikely) is excess cable friction in which case the shift cable+housing need replacement.