nagornyi,
As you have found the converters are unreliable. A mainboard without SATA ports must be very old, I would consider replacing it before buying an IDE hard drive, the other solution.
As a rule, using an adapter to make new tech fit older products (like 20-to-24-pin PSU adapters, PS/2 to USB etc.) is not advised. It may work, but perhaps not as well as it could. In some cases it could be disastrous, destroying gear at one end or the other.
People might post saying "this adapter worked for me" but it may not work for you. Are you positive that the drive is in working condition? Is the correct power adapter connected? Can you hear it spin up when you turn on the PC?
Tony
"...an eye for an eye leaves everybody blind" - M.L. King