Hustler will not run

I have a Hustler Sport that seems not to be getting enough gas. I took the the bowl off the carb. and cleaned the white plastic and float, still don't work. I don't understand the electrical part on the bottom of the bowl.

Sounds like your carb has an anti backfire solenoid on it. It is designed to cut off the fuel supply in the main jet of the carb after your have turned the key off. The solenoids do sometimes get stuck causing thus causing an inadequate flow of fuel through the main jet. Might want to see if you can see the solenoid moving when you turn the key on and off.
Push Lawn Mowers | The Practical Consumer

I unscrewed the solenoid and pluged it back in, when I turned the key it sucked in.

Cleaning just the float probably isn't enough. Most of the carburetors that I've seen that needed to be cleaned also need the main jet cleaned. The best course of action is to find a youtube video on your specific carburetor and watch it until you feel comfortable doing what the video teaches. TAKE PICTURES and/or draw diagrams of everything including carburetor linkage/springs/etc before disassembling so you can get it all back together properly. Keep in mind that this may not fix your specific problem as the cause could be something else but in your original post you say that is seems to be not getting enough gas and one of the most likely reasons is the carburetor. Did you happen to change the fuel filter?