Residence card in Denmark?

[Fatdane]

So my girlfriend and I have decided it's about time to build a life and a family together. Meaning, for starters we are getting married - Yeeey!
But as much as I am happy about this I'm extremely worried about the process of obtaining a residence card in Denmark. The current situation is that I'm not an EU citizen but I have the right to enter the schengen zone and visit for 3 months. So I have previously visited my Danish girlfriend without the need for a visa or whatsoever. Now If I'm being honest the statsforvaltningen(State Administration) has been of absolutely no help when it comes to the process of obtaining a residence card(They are basically telling us YOU CANT STAY). So I was wondering if someone could share experiences and maybe point us in the right direction in weather we should be trying to obtain a Danish residence card or a residence card under EU law. Because as the situation stands the statsforvaltningen keeps saying I have to visit every 3 months, I cant apply for EU residence card because my partner doesn't live outside DK so EU law doesn't apply to us and that we can only apply for permanent residence card under family renunciation for which we obviously don't have the requirements (something that they point out with joy). Thanks for any help in advance!

[CR001]

You will need to follow the Danish national immigration rules for joining a Danish spouse.

[Fatdane]

Well the reason they are saying we can't get the residence is because she was on kontanthjælp(few months of social benefits). But on the website it says that it MAY be a problem. So If someone has experience with that an advice will be greatly appreciated.

[mgb]

Maybe you can get a residence permit on your own rights via a job or something else.