Probably good to start with the service manual. You will need the model# and the serial#. I prefer to go direct to Cummins Sales and Service 800-286-6467 but it is possible to get the service manual from other sources using google. If you call Cummins, they will usually send a FREE copy of the specific service manual to an email address.
The age of the generator would be of a high concern. I would first make sure that the engine is turning freely. I cannot say exactly how to manually confirm this on your model, but it would be best to first figure out how and check the motor. After that it would probably come down to the starting circuit and components of. The starter is obviously on the top of the list since you replaced the solenoid. You can check the solenoid for proper operation with a multi-meter.
You will also need good and charged batteries to start the generator. I would make sure the batteries are fully charged as there will be extra power needed to turn over a generator that's been sitting for a few decades. Usually, the generator is wired to the house batteries but you should verify this, so you know where the power is coming from.
What exactly are the symptoms when you push the start button ? What do you hear or see ?