Brain Host

I am hoping you can direct or advise me on what to do or where to go from here.
I have an issue with Brainhost.com who have hosted my domain injectionmouldingtips.net
My site was never up more than 70% of the time (accessible on the net) confirmed through 4 different computers each with their cache cleared. After numerous support tickets raised I decided to goto godaddy to host my site, they require epp and authorisation codes. I raised a support ticket (high priority) asking for those codes, within 24 hours it was marked as 'customer reply' whatever that means. My site was offline 100% of the time from that point on, (that was 2 weeks ago) they haven't replied to the ticket, my site has since expired and they have now charged my card with a fee for 2 products that were cancelled months ago. I have gone back into the back office and found they were switched back on. However, firstly I have an email that states the cancellation of these products, but more than this...why charge for products relating to a domain that has now expired? I cannot go through visa to start an investigation because (at the moment) these 2 products were turned on so Visa will say I authorised them. I cannot transfer my domain name to godaddy because I require the release codes from brainhost.
I am being held to ransom and I might lose the domain name to some-one else.
I have named and shamed on [redacted] but that does not get me access to my domain name which I (supposedly) own. I also paid a $197 us dollars for lifetime hosting. I thought you purchase a domain name once and pay for hosting periodically.

Please advise me on where to go from here.