Trouble starting my Vulcan 500?

I parked my bike and left it for a few hours. When I returned, I hopped on and turned the key on. However, because I was on an incline, the bike rolled back about a foot. I then hit the start button and it just wouldn't turn over. Finally, after I pushed it forward about a foot, it started up just fine. What's going on??

Also, about a month ago, I finished fueling up and got on the bike to start it. I turned the key, the lights came on like normal, but when I pushed the starter, it clicked and everything died. I mean, the bike just went completely dead, no electrical or anything. After several minutes, I would turn the key and the bike would light up again, but when I pushed the starter, it would click and die once more . Finally, after going through this about 3 times, I turned the key, the bike lit up and started just fine.

Sounds like maybe something with the starter or the relay, but I'm not sure. Any suggestions?

Clean and tight the batteries connection and starter wire connections then you might need a new starter, any mechanic can check how many amps your starter is drawing while starting ,that tells the state of the starter.

check all of the elec connections in the start circuit. one of them could be loose or corroded. start at the battery connections.
you didn't say how old it is, could be a worn key switch or the start button switch could be failing. these kinds of problems can be tuff to locate, so be patient & thorough
using dielectric grease on elec connections helps prevent future corrosion

Could be loose or dirty battery terminals, or battery terminal at the frame/engine ground - clean the terminals and wire connectors with a wire brush.
Defective ignition switch.
Weak connection "to" the main fuse.
Defective main fuse.
It's unlikely that the starter motor, starter solenoid, or start switch would have anything to do with the entire bike going dead.
The head light, horn, indicator lights work off of a different circuit.
It would take the previous items to cause the entire bike to go dead.
The amperage draw of the starter motor would be enough to cause a faulty connection to arc and sever the connection - when the connection cools down it could temporarily re-connect.

When the bike goes dead, you can trouble shoot the electrical problem with a test light.
Attach the test light to ground.
Touch every connection in the path of the electrical flow.
Battery (+)
Solenoid
Fuse box
Main fuse - both sides
Ignition switch connector "power into switch".
Key on - power out.