I just bought a Buddy 150 from a close friend for $100! It only has 1,200 miles on it. It was in a mild crash once and was completely repaired by his insurance. He rode it for a bit more ,and then let it sit in his garage for 2 years.
First let me say this is my first time working on a bike
Here is a clear sequence of events
Put fresh gas in
I replaced the battery with a new one (yes, it was charged)
We tried to start it- ignition clicking noise, with a small sound of wanting to turn.
We kickstart it- it starts and dies within a few seconds
We try ignition again- it starts and dies within a few seconds
We try a few more times- sometimes are more promising but it will die even if we pump the gas to get it moving, or just let it sit.
We leave it for two days...
We try again- there absolutely no response other than a farting sound in the ignition. The lights work, the horn works.
We try kickstart- nothing
We think maybe the battery lost juice from us trying so much and jump it with a car for good measure (no we did not turn the car on and fry it)
It gives one turn over and dies. no further attempts work.
Being the crazy adventurer that i am I push 5 miles to my house at midnight so I can have it at home

I check the spark plug- No spark using ignition, very weak spark when I kick
I replace the spark plug with a new one- same results as old one
I try the horn- this time it does not work, just a farting noise
So again, at first wanted to turn and would die quickly and the horn worked.
Now
-weak spark in plug during kick, no spark during ignition
-ignition just makes a farting noise
-horn makes farting noise
I am reading the user manual and the service manual and I have an intuitive sense of how this all works but I am having trouble finding each thing with out a detailed diagram and a knowledge of the names of parts
I want to make sure gas is getting to the Carburetor but have no idea where the carburetor draining screw is.
I want to check the solenoid but I am not sure where to find it. Is it that black case right above the starter coil? The one with a one large line connected to the face and a smaller line connected to left side of it? all the pictures of solenoids i see have both lines connected to the front face so I am not sure this is the right part...
Thanks for any help you can offer, I do appreciate it