Sorry, couldn't resist but joking apart, the story seems somewhat confusing. Let me see if I understand all the combinations:
1. The PC failed with the original graphics card
2. Replaced the failed card with the GT 640 and the machine won't boot Windows at all
3. The machine will boot a Linux system off a Live CD/DVD with the GT 640 in place
4. The machine will boot to the Login screen without any card installed
5. The state of the Motherboard capacitors is unknown (at least, I can't find a check)
6. The TOTAL power requirements of the machine with all installed devices is unknown
7. Your brother has a similar card installed in his machine and is working but we don't know how his machine relates to yours.
I'd be inclined to rule out the capacitors, the machine works under Linux Live CD and without a graphics card, so they may or may not be weak but not a killer.
The motherboard appears to have an onboard graphics chip that will at least take you to the login screen - is that the Windows login screen or the POST login screen? No matter, something is driving the screen.
If there is an onboard chip, why won't Windows use it? Has Windows been setup in some way to ignore anything but the add-in card?
What is the Live Linux using to drive the screen? The onboard chip or the GT 640? Live systems are both very flexible and very basic - they'll use whatever they can find, which is what makes them useful diagnostic tools.
Does the BIOS recognise the GT 640? If it's blocking it and Windows is blocking the onboard chip, you aren't going to get far.
Do we KNOW the motherboard is working? Probably, Live Linux and the boot to Login work but we don't know for sure that the PCIe slot is working.
Do we KNOW the GT 640 is working? No, unless you are absolutely sure the Live Linux is using it.
Do we KNOW you have adequate power from the PSU? No, unless you've done the sums for the full system.
Suggestions:
1. Ask your brother to test YOUR GT 640 in his machine - that will rule the card in or out.
2. Check your BIOS settings.
3. If you have access to the power supply such as Bob mentioned, test your machine with both your add-in graphics cards to check whether the issue is, as most suspect, power and if the original card has actually failed.
4. If you have the space on your hard disk, partition 16 GB off (use something like Partition Wizard on CD or similar) an try to install windows from your install disks into the new partition with the GT 640 installed. If this works, then your problem is with your production Windows system. If it installs and works, load the latest driver for the GT 640 from Asus/Nvidia. If all this works, back it up your production partition again and try a repair install.
5. If none of this works, I'd suspect the PCIe slot on your motherboard.
Hope some of this helps - if not, as Bob suggested a few posts ago, it may be time for professional help.
Good Luck!