After updating Asmedia drivers, my external HDD isn't working  

Gil mate have you tried the drive on another machine?

I presume this is happening with your front USB ports? I'd suggest making a backup of the latest driver, remove all USB 3.0 devices and uninstall the Extensible Host Controller (expand the Universal Serial Bus Controllers tree in Device Manager). This is the mid board header controller for the front USB 3.0 ports. Reboot and Windows should recognise the device and reinstall it, then install the backed up latest drivers again and give it a whirl.

As Boozad says mate you need to look again at he drivers for thatboard which I see is a DDR2 driven one are you sure of the board number?? as Ididn't think USB3.0 came out until after DDR3 was the standard RAM I stand tobe corrected of course.
Now looking at the specs for that board it only has 12 x 2.0 USB port there are no 3.0 USB ports on it. Doesn't matter cos the 3.0 is back compatible.

GIGABYTE - Motherboard - Socket 775 - GA-EX38-DS4 (rev. 1.1)

We need some clarification here Gil as your OP says an ASUS P8Z77-V deluxe motherboard whereas your system specs say you have a Gigabyte motherboard which John has referred to.

If it is the ASUS board you're having problems with then please follow the steps in post #4 regardless of the position of the USB ports. ASMedia controllers are normally controlling mid board headers on AMD systems, the fact you have an Intel system with the ASMedia controller controlling the rear ports doesn't really make any difference.
Did you download the drivers from the ASUS website? You may have to download ASMedia drivers from elsewhere as it's been a known issue in the past that manufacturers don't carry the latest ASMedia drivers on their websites, I had the same problem with my backup AMD rig.

Gil said:

Ddues :) how did you get that I have Gigabyte mobo?

Ok... writing these lines I think this mobo is in my profile... that's the old mobo I had... I'll update that

I did explain that in my last post.