invalid checksum (Kernel Panics and 10.7.4 update)

Dear all,

Not new to mac but new to this forum so i'm sorry if I am maybe in the wrong section! (I tried to search other awnsers but couldn't find any alike).

I have a reasonably new Macbook Air (december 2011) with lion 10.7.3

I was recently having a lot of kernel panics and I couldn't start up, not even in safe boot and couldn't enter disk utility before a kernel panic would occur. (I do not know how to copy the kernel panic information as my computer will do nothing else but shut down when they happen)

When I wanted to reinstall from my time machine, I couldn't see my own harddrive to copy the back up on (only the free partition on my la cie) but I could repair and verify all disks in disk utility (which I did multiple times) so I did that and started in safe boot (without recovering from harddrive). I hoped that with installing the osx update (10.7.4) the problems would dissappear because next to apple applications, office, skype and vlc I wasn't using anything else when the kernel panics started occuring (not even my extarnal harddrive). I deleted skype and tried to download OSXupdates but they kept getting interupted because my connection is very bad (I am in Burundi at the moment) so I installed Igetter and managed to download the 10.7.4 combo packages (took 36 hours) but when I tried to open that it said that it had an invalid checksum, normally I would give up and bring it to my apple reseller back home but I don't have one of those here;)

Anyone can please help me out?

(Do I need to give more information?)