From what I understand the Miners are responsible for veirfying the accuracy of the transactions contained in a block
No. It is not the miner's job to verify transactions; that job is for the full nodes (of which miner's are a subset). Miners do not determine what valid transactions are. Their only purpose is to order transactions and, when there is a conflict, say which came first and is the correct one. This ordering is also subject to certain restrictions and all blocks are validated by full nodes.
and as a reward the quickest one to come up with the correct hash earns Bitcoins. Maybe it's a stupid question but what will happen to the Bitcoin network once all 21 Million Bitcoins are in circulation and there is no longer an incentive for Miners to operate their expensive and power hungry rigs, who exit the system after selling their Bitcoins? Who performs the transaction verification then? Or will Bitcoin grind to a halt when that happens?
No, that is completely incorrect. As I said, transaction verification is done by full nodes. Secondly, each transaction pays a transaction fee which is rewarded to the miner that includes the transaction in a block. So transaction fees will replace the block subsidy in the block reward.
