I dropped my P&S, and now the zoom barrel is like this:
It's out of warranty, what's the best way to fix it?
Take it apart? Hit the barrel with something? Push it?
Please, never user a hammer to fix your camera. Even a simple P&S has too many components that can be further damaged by hitting it, and the odds that you'll hit that miracle spot that will fix it are very low. You know, $50 bucks for hitting, $500 for knowing where to hit...
My first advice would be to take it to a store and ask them about how much would it cost to fix it for you. Depending on where you live, they'll estimate the cost without charging you just for that.
But the thing that I would do, if it happened to me, would be:
1 - unmount the camera too see how bad that was, if there was damage to circuits, etc., and perhaps try to fix myself
2 - see if some parts are still reusable and perhaps sell it online (like eBay or something) as spare parts
3 - buy a new camera and be glad if someone bought the broke one as spare part.
From the image you have posted, it seems that the gears in the zoom lens are broken, it will not be possible to fix this, however, you can try to replace the whole lens assembly. The replacement part is on sale for USD 53 here.
P&S cameras are generally tightly packed and hard to put back together when opened. I would recommend discarding the camera so as not to sink any more money on it and buy a new sub100 compact.
PS: Hitting probably will not fix the camera but would surely be fun.
You can try to take it part which is the only sensible thing to do for this camera. Even if you fix it, some components are broken, so it will never be the same.
Repair is out of the question because it will cost more than the camera itself. Once I brought a $119 camera which my daughter broke and they asked for $150 to fix it. I said, that it was more than the cost of the camera, so they said to buy another camera.
You dropped it, so even if it was under warranty, they would not fix it.
At this point, considering it is such an old camera, you can easily buy a new sub-$100 camera for less trouble or consider this as a great opportunity to upgrade :)