"Dried up" means that something has ended, in this case the Man couldn't find work (like he seemed to be able to in the past), or maybe he lost his job due to Denver, Colorado experiencing a recession. A "recession" happens when there is decline in the economy, usually in trade or industry. This results in people losing their jobs because of being laid off, and/or when businesses close for good. People become poor, and towns become poor as well.
If you don't have people making money, then the town doesn't need banks because there is no money to put into them. Eventually everything closes down and/or people move away to try to find work elsewhere – like the Man seems to be doing when he goes to the employment agency.