If you're still in the soup, you need to climb to MSA and dead reckon to the missed approach point then dead reckon the missed approach procedure. While you're doing that, I'd attempt to establish some kinda radar contact with center, approach, whatever and get a vector. Declare if you need to.

This actually happened to us (sorta) a few weeks ago. Going into an airport with only a GPS approach. Our GPS went blank somewhere outside the FAF (about a mile outside the FAF). I started a max performance climb to MSA while dead reckoning the final approach course as much as possible and called approach, told them the situation and got vectors back around. By the time the GPS came back up, they were able to turn us onto the course and we flew the approach with no problem.

-mini