The following banks and credit unions offer excellent features and benefits. While we recommend them, they are not our top picks for the simple reason that they are not guaranteed banks. They have however helped a lot of people, and may be able to help you too.
Many people have been able to get accounts with TCF. They use ChexSystems but are extremely lenient, definitely worth a chance.
First Dakota National Bank
They do not use ChexSystems at all. Generally they pull Equifax.
Farmers and Merchants State Bank
All that is needed is an ID and SS card. If you request a debit card they will run a credit report
Dakota Plains Federal Credit Union
They run OFAC and TeleCheck to verify new accounts.