I'm not sure exactly what you are asking, but it sounds like you are describing mining.
In mining, you attempt to solve a block to be added to the blockchain. If someone else solves and broadcasts a block before you do, then you have to start over with a new block. If you run through all 4,294,967,295 possibilities without finding a solution, then the block you are working on has no solution, and you have to try a new block.
So, your computer will keep working on more and more blocks continuously, and if you are solo mining, then you'll get paid for the blocks you solve. If you are mining in a pool, then you'll get paid for the effort you put in even if you are not the one who solves the block.