Motorcycle Repair: Solenoid, honda v65 magna, jumper cables

Question
I have an '86 Honda V65 Magna. It was running fine until one day it wouldn't start. I have recently replaced the battery but when I turned the key to the start position, no instrument function at all...no headlamp either. So I attempted to jump start. It started just fine. I thought cool! It's a battery problem, I can get it home and work on that. But - as soon as the jumper cables were removed the bike died and wouldn't restart unless via jumper cables. I checked the solenoid cap and fuse. The cap was melted but the fuse is good. I got some new connectors and attached the wires to the spades on top of the solenoid without the plastic cap. Once again, the bike will start and run as long as it's hooked up via jumper cables. As soon as the cables are removed, it dies. I figure I may have to replace the solenoid at this point. I just wondered if there is anything else I need to be looking for?

Answer
Solenoid and Main fuse are good places to start.
BTW, when you were boosting the bike with the cables, was it hooked to a car battery? If so, was the car running or turned off?
When boosting a motorcycle battery from a car, the car needs to be turned off. Otherwise it will 'cook' the motorcycle battery.
I suspect that if the solenoid and main fuse are good, then you might want to grab a known good battery and try it.