2001 GZ won't start

[sqrimp]

Hey guys, I'm new to this forum, and bikes in general as this 2001 GZ250 is my first one.

Background info:
I bought this 2001 GZ250 with 8k miles on it, and it started fine. I took it to my storage garage and kept it there. 3 weeks later, I came back to take it out for a spin. This is where things go wrong, and it won't keep an idle. It would idle maybe 1 out of 10 attempts to start it, and would eventually shut off.

Details and things to note:
1. The kickstand is up, engine switch is on, it is in neutral, and clutch is engaged.
2. The choke was turned on because it was a cold start.
3. The starter turns and cranks.
4. The battery started dying after constantly trying to start it, and had to be jumped with a car a few times because of which.
5. The carb was extremely clean.
6. There were some particles trapped in the fuel screen filter.

I'll admit I am savvy with fuel injected cars, but tinkering with a carbed bike is a whole new ball game for me. If there is any information I'm missing, please ask and I'll try my best to answer. any help is appreciated.