I'm seeing that other threads have been posted on this issue, and the most common "fix" suggested for it is to actually purchase Minecraft. What if they have, and for some reason it won't let them log in, like the issue I have. My old laptop (which was Windows 7 x64) that I used a couple months back ran the Technic Launcher without any problems. Other people with the issue don't seem to have Windows 8, and I can't really compare Java versions since they say "The latest", which could of meant anything really.
I'm going to see if I can use someone else's login details to see if it's just my account that it refuses to connect, or if there is something stopping it. I'll edit the OP with anything that comes up.