Yes it does. I mined solo with my 5850 at a difficulty of 3 million at the time for several months, I didn't find a block. Was that electricity not wasted since I didn't even help the network?
What you were doing by expending that energy, was decreasing the chances (read: probability) of a malicious attacker with 'x' amount of hashing power from being able to perform an attack on the bitcoin network (read: payment verification network).
Some of those were my payments, and I paid fees for that protection. Not wasted at all, I think.
The "miners" simply guess random nonces until one is found that will produce a valid hashed block. It's similar to throwing spaghetti against a wall until one keeps sticking to the wall and declaring that one the winner.
