I'm having the same problem using XP (32-bit).
Run launcher > Launcher says "checking launcher version" for a second > Disappears without doing anything.
Not sure what the problem is, and I'm fairly fluent with computing generally (just not with Java!)
No rush for response, but would love to get playing after watching the Yogscast Tekkit videos
Using ESET Smart Security (firewall and anti-virus) if that helps?