On a cold day at sea level, the 310 should be able to get at least 200fpm. The book number is about 300fpm. However, they may not have been going fast enough to get book performance, and a plane that old usually can't make nearly the book numbers. They hit at about .3nm from the end of the runway, significantly left of the extended centerline, and at an altitude of about 100 feet. That would be consistent with a climb rate of about 150-200fpm.
My guess is that the left engine failed. The left engine is the critical engine, and so the plane would have very strongly wanted to turn left. It would have been slow having just taken off, and so the pilot probably had to turn to keep his speed up and maintain a positive climb rate. He probably either forgot about the power lines, or was just hoping to clear them since he couldn't see them.
Sadly, this is probably just another instance of the second engine being just enough to get you to the scene of the crash.
In most light twin planes, both props turn the same direction, and so the plane has a natural left-turning tendency when climbing. If the left engine goes out, you're in a very bad situation, because now the plane really wants to go to the left. If you indulge it, you don't get to go where you want. If you don't, you may get a worse climb rate (which is already very bad.)
Even simple accidents are usually remarkably complex to piece together and almost always start with a very simple small thing that by itself would not be enough to cause an accident. The follow-up to that first thing is just as important, or possibly even more so.