Thanks for the reply. I already have that BIOS installed, and have tried different eSATA cables. My PSU is 450W, which I think is more than enough, considering I don't have a graphic card (or any other card), nevertheless I have no problem connecting additional two external USB hard drives.
I want to elaborate on the problem: I am not connecting an external eSATA device, but a regular internal hard drive, with internal power supply and the external eSATA port. I am using a eSATA to SATA cable. I don't have another device to double check.