Do all bills affect your credit rating or just credit-related bills (such as creditcards, loans, mortgages..)?

I understand that credit card accounts, mortgages, and things like car loans will affect your credit score majorly depending on when you pay, your balance, etc... But how much, if any and when, do other bills (insurance, internet, phone, medical..) affect it? And if they do, will paying them off fix this? I... show more I understand that credit card accounts, mortgages, and things like car loans will affect your credit score majorly depending on when you pay, your balance, etc...
But how much, if any and when, do other bills (insurance, internet, phone, medical..) affect it?
And if they do, will paying them off fix this?

I recently was denied an application for a regular checking account at Bank of America. I thought it could be these reasons:
My current bank account is -70.71 and I have put a hold on it until i close it.
My insurance through Progressive had one monthly payment left on the policy and it was never paid.
My internet through Sprint was a 2yr service agreement and I failed to pay the bill 3 months and was therefore terminated.
My credit card is pretty much maxed although I pay the bill on time.
I have a few outstanding medical bills (under $500).
HOWEVER, I ordered a credit report through Equifax and ONLY my credit card account info is shown! What about everything else?
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