Win Vista/7 32 bit works, but Win 7 64 bit keeps crashing

Hi,
I ran Win 7 64 Ultimate bit on the same computer for a year with no problems. One morning my antivirus wouldnt update anymore. Later on Firefox and Explorer started to crash. Tried to restore system - more problems appeared. Decided to re-install windows as I had done many times before.
Installation crashed, blue screens apeared on several re-insallations. If I managed to install windows updates would not install and programs would crash.
Vista 32 bit and Win 7 32 bit Ultimate work with no obvious problems - dont crash on installation and updates can be installed with no problems.
Updated BIOS, swapped memory sticks to check if any of those is faulty, used different memory slots. Everything seems ok.
I have been trying even different installation discs, still the same 32 bit work, but 64 bit doesnt,

System:
ASUS P8 P67 LE
Intel i5 2500K
2x4GB Team Elite 1333 Mhz RAM
Corsair Force Series 3 120GB SSD primary drive
Sapphire RADEON HD 6770 1GB

Any ideas?

Thank you

you have 3 different OS's installed? which drive is windows 64 on?

I dont have 3 different OS's. I have been installing them one at the time on the same drive. By doing that I was just trying to see what works and what doesnt. I have never had more then one OS installed. Vista 32 bit and Win 7 32 bit work, but when I try to install to install Win 7 64bit problems start to appear.

Where did you get Win7? How is it activated?

Confirm the official ISO and burn to DVD using ImgBurn at 4x speed.

Wipe the HD using Diskpart Clean Command before following these steps to get a perfect Clean Reinstall - Factory OEM Windows 7 - the steps are the same for retail.

I have been using two different installation discs (borrowed one from my friend), used flash stick as well. Results are the same. As I mentioned in my original post, I have occasionally managed to install OS Win 7 64bit, but every time there are problems with windows updates and system generally even when I have managed to install actual OS.
I have no such problems when Vista 32 bit or Win 7 32 bit are installed and ran on the same computer. And I had Win 7 64 bit installed and running on the same computer uptill these problems started.

How is it activated?

Test your RAM for 5-6 passes or overnight with memtest86, not just swap slots.

Test your HD using maker's HD Diagnostics extended CD scan followed by Disk Check.

Stress test your processor with Prime95.

Links are in my signature below.

I will run tests you suggested and let you know of the results. It might take a while.

Thank you

Follow the steps in RAM - Test with Memtest86+ to isolate the stick or slot which is the problem, then replace it or don't use the slot.

Will do