Minecraft start problem

First thing's first, make sure you have Java, it doesn't have to be the latest build as on my Gaming PC i haven't updated Java since Minecraft first came out and it's been fine (apart from a notice saying i need 64-bit java for a full render distance) but it's best to get the latest build just in case, if you do have java update it, the problem could be your Java installation and an update would fix that, otherwise uninstall and reinstall java

Second, if your reinstalling Minecraft, make sure you're online, while you can play Minecraft offline that's only after you've downloaded the files, while i haven't upgraded to 1.6.2 (because i would have to regenerate the world to update it and i'm waiting on the new biomes in 1.7 before i go though that) i'm assuming you can still play it offline just by failing to login and selecting "Play Offline". if you can't connect to the internet on your computer you can just run Minecraft on a computer connected to the net to download the files and then copy your .minecraft folder onto a memory stick and transfer it to your offline computer

if you're still getting an error, redownload the Miecraft.exe, i do remember that if you was using the old launcher it wont automatically update to the newer one and you had to download the new launcher manually however that's easy to do since you can just log into your account on the website and redownload it since you are using a legitimate copy

After it freezes you could just leave it open for a few hours or something and don't do anything to it. Sometimes it just takes time to fix.