Hey, it started working. What I did:
1. Manually downloaded (as in placed the link in an internet browser) lwjgl.jar and lwjgl_util.jar files from the links provided in the log and placed them in my \.techniclauncher\technicssp\bin folder.
2. Deleted minecraft.jar in the same folder.
3. Launched the launcher, it downloaded everything and minecraft began to work.
All of that was probably stupid and pointless because I then reinstalled the technic pack and it worked perfectly without a hitch (Note: I DID try reinstalling earlier today and it white-screened then), so probably it somehow just got fixed by itself :D
