Unfortunately I had to do the same thing one morning. It was 50F and rained during the day, and then it got down to 20F at night and froze my car completely shut. I had to crawl in through the trunk and it sucked!
iv had the same exact problem in my 97 ex for a few months. its not frozen, its in southern texas. lol. cold day in hell. so i guess its the electrics. im stationed way out here in LA for a little while but my wife still needs it fixed. so theres just a plug to jostle with near the hinge? im going to try and explain to her how to fix it as soon as i find out.