Although you may get better than you have now by buying something, most SLR's struggle with the situations you have described. I am not saying it is not worthwhile, just don't expect miracles from a PnS. Flash pictures generally look terrible in these situations too. You have nothing to bounce the flash off, so it will be direct flash. Direct flash always looks like direct flash (deer in headlights look).
To shoot a concert from the pit and have a reasonable proportion of acceptable pictures you are probably looking at close to $1500 in SLR gear. You can get great shots with less, but the majority will be quite poor. To shoot from the audience, even more money is needed. Turn off any on camera flash, it will just light up the people around you and put nothing on the stage. If you have an external flash, it can be used, but the shots still won't look like what you are experiencing at the concert.
Again, I am not saying that you can't get good shots, just expect nothing and be happy when you get something.
EDIT: To try to get low light pics, turn up the ISO on the camera (this will increase the shutter speed and helps you avoid motion blur in your shots). Higher ISO will give you more noise (especially in a PnS), most SLR's can shoot at 800 or 1600 without unacceptable amounts of noise, most PnS that I have used (I am not saying all of them) look like hell past ISO 200. Basically, if you want a clear picture say you want a shutter speed of 1/100 (just an example) of a second which a DSLR and enough money may give you, with a PnS, your shutter speed will be 4 to 8 times longer (ie 1/25 to 1/12.5 seconds). At those shutter speeds, almost every shot will be blurry. Unfortunately the best way to improve low light performance is a bigger sensor, bigger sensor requires bigger glass, bigger glass costs more money and PnS are incredibly budget sensitive so they go with small noisy sensor and small glass. Hope this helps a bit.
