I tired with a debug build, but I'm not sure if my log is going to show anything useful since the mission didn't even start. It's attached anyways though.
Um, that log? Haha - oops, too soon on the reply!
Also, from the "Malloc failed" message, you might have a corrupted pilot file. There was a bug in earlier versions of BP that could cause this, it's been fixed in more recent versions. Luckily for you, you're almost at the end of Act2, so you can just play the last mission from the mission simulator - press "ctrl-alt-s" from there and you can see/play all missions in the campaign. However, to continue with Act3 you should probably upgrade to the most recent BP executable (see the stickied compatibility thread" and create a new pilot.
Anyway, regardless of all that, a log will confirm if I'm on the right track here or not.
Edit:
Are you sure that's the correct log? It doesn't show blueplanet2 being used as a mod?
FreeSpace 2 Open version: 3.6.17.9481
Passed cmdline options:
-mod blueplanet,mediavps_3612
Anyway, the FSO version you have does contain that bug I was talking about, so you should follow the steps I outlined above:
1) play the last mission from the techroom with ctrl-alt-s
2) update to a newer BP build
3) create a new pilot for BP2 Act3