How do you have your drives configured in the BIOS?
SATA Ports must be set to AHCI or RAID configuration. If you're not in a RAID setup then set them to AHCI, eSATA will NOT BE recognized any other way.
Does your Asus motherboard have the BIOS setup guide in the manual for AHCI?
Make sure the hard drives are NOT configured as "IDE" setup.
Your listing for the Asus motherboard model is not accurate... I think. I believe you might have a M4A78-EM board. See the photo below for all the mobos at the Asus website with model numbers similar to yours.
Download a free application called:
SIW - System Information for Windows. Click the link to get the free version:
SIW 2010 (build 0428)
It will tell you just about everything regarding hardware, motherboard make and model, RAM, software, hard drives, brand of your favorite wine, etc.
This is a Snagit capture from the PDF of your owners manual. Nearly all BIOS have similar settings and configurations.