There is a serious bug with an auto-update for the Technic launcher which leaves you unable to run Tekkit Classic, if you are currently logged in I suggest you don't disconnect unless you have to.
If you've already received the update (like me) and have this problem then I'm afraid it's just a case of waiting for a fix, it's also worth mentioning that the bug affects Windows, Mac & Linux.
UPDATE: 21:35 - This bug also seems to affect other mod packs for some, it appears the launcher is trying to connect with Vanilla Minecraft instead of the correct modpack.
UPDATE: 22:20 - Still no fix or work-around, I'll be giving up for the night soon :(
UPDATE: 22:40 - Giving up for the night, hope this is fixed by the morning!
UPDATE: 21:35 - This bug also seems to affect other mod packs for some, it appears the launcher is trying to connect with Vanilla Minecraft instead of the correct modpack.
UPDATE: 22:20 - Still no fix or work-around, I'll be giving up for the night soon :(
UPDATE: 22:40 - Giving up for the night, hope this is fixed by the morning!