If I filed with another agency to apply for the refund advance and was not approved can I cancel that refund and file with TurboTax?

That depends entirely on what you signed with the other tax preparation agency.  Did you read the contract before you signed it?  Read it now.

If you were not filed then you can start again on the TT system ... so did you sign a form authorizing the filing of the return ?   Or was this all done off last pay stubs ?