When you say that you are "bypassing" the solenoid, if you are placing the positive cable to the (+) side of the solenoid, you are not really bypassing it. If you are placing the positive cable from the power pack to the large solenoid post nearest you (+), then all you are doing is applying dc power that would have been applied by the house battery if it was working properly. The solenoid has two large posts. One of those posts is for the positive battery cable that comes in from the house battery. The other large post goes to the starter. In order to "bypass" the solenoid you have to directly tie the two large posts. In the old days, we would have used a screwdriver blade to bridge the two posts, enabling 12 dc current to flow, sending current to the starter. If you hear the solenoid clicking, you know most likely it is working, however, there is also the possibility that it could also click if the coil inside is unable to make full contact to connect the two large posts sending power across. You can touch it with your hand while you crank the generator and you can feel it clicking. The clicking sound made by the solenoid generally indicates insufficient 12 vdc power. I agree with others that it is mostly likely the house battery, if that is what powers the generator, but you also not discount the negative and positive cables.
