You should to disable only channel with the problem HDD, not for system drive channel
Okay on my end, in Device Manager, without the eSATA adapter and any HDD connected, under IDE/ATAPI controllers, I see 2 "ATA Channel 0", an "Intel(R) 82801G (ICH7 Family) Ultra ATA Storage Controllers - 27DF", and a "Standard AHCI1.0 Serial ATA Controller". Under Disk drives, I see only "FUJITSU MHW2080BH PL ATA Device". With the adapter and problem HDD (WD drive; WD10EAVS-00D7B0) connected, Disk drives and IDE/ATAPI controllers remains the same. However, there is the addition of Storage controllers which contains "JMicron JMB36X Controller".
When I connect a secondary functional HDD (a HITACHI HTS547575A9E384) instead, Disk drives now also contain the "HITACHI HTS547575A9E384 SCSI Disk Device". IDE/ATAPI controllers and Storage controllers however remains the same.
So when the problem HDD is connected, which one should I disable? Or how should I disable the channels only for the problem HDD? Do you need screenshot(s)? I currently cannot upload the screenshot(s).