Same thing recently happened to my 3GS as well at my first iPhone 5 - Apple Store charged me the screen replacement cost and gave me a new 5. I had given the 3GS to my brother after he killed his Blackberry a couple of years ago and I finally got it back in November. Traded for a Russian Imperial Stout I love 😀. It had been powered off for a while (He had a 5S and now a 6S since) and when I charged it the battery drained 40% sitting overnight. I charged it the next day and the battery swelled. Fortunately (since I intend on keeping the phone now that I have it back) it didn't bend the logic board as much as the OP's, it instead pushed the plastic back away from the metal frame. I've since had the broken digitizer fixed (I replaced the battery with an iFixit one) and I'm picking it up from the shop tomorrow. I've got a 5 now and there's a 6S Plus under the tree but I'll still be glad to have the 3GS back since it was my first Smart/iPhone back in '09. I hesitate to say it's a sentimental thing, but I will be happy to have it back in my custody.
Does your phone still work Nick, assuming you were brave enough to test it?