You could as well try a new cable and do like Duane suggested: connect it to the board before replacing it, and try to see if it works properly. Then replace it. You probably have a damaged or defective power/mute/volume cable because Volume Up/Down functions on the board have a different circuit from the Power On/Off circuit - UNLESS you have a damaged connector where those 2 functions meet; that would be the connector that connects the cable to the logic board;
Or that connector is dirty (clean it with a cotton swab dipped in 90%+ isopropyl alcohol);
Or the cable is not seated properly: disconnect then reseat the cable.