In desperate need of help with 2000 Ducati Monster750 Dark

Hi guys~ I need major help with my 2000 Monster750 Dark.
It just won't start.... even if I get it to start, after it warms up, if I give a little throttle it make very weird muffled sound like air is trapped and engine dies. Once it dies, if I try to start up again, it just makes clicking sound like the battery died or it's really low so it makes you think the bike is not starting because of the battery.
So at first, I thought it was because of old battery so I replaced with brand new one and the first day of putting the new battery, it seemed like it was working fine. But next day when I tried to ride the bike, it started all over again.
It just won't start even if it did, it died right after I give a little throttle and the clicking sound continues when pushing ignition button. I know it's over 10 years old but has really low miles around 9200. The Ducati dealer I bought from told me it's been serviced and has no problems at all but now look at it... I just don't know what to say. That's why I need major help from you guys~
I just have no idea what the problem is... and I'm really low on cash right now so taking it to the dealer or the shop is out of the question. I'm trying to fix it if I can do it.
My best guess is either charging or ignition system or the carburetor is gone bad, or spark plugs maybe...
I really don't know. I would love get some help and advices from the forum members how to go about this problem. So please leave any kind of messages that can be useful for me to use.
If any members who loves to fix or work on a project and lives around Seattle, WA. area, would so kindly come and take a look at my bike I'd appreciate it very much. I'm in Federal Way just south of Seattle. Just drop me a line~ anyone with great mechanical expertise will be really helpful~ If someone who lives nearby come to look and fix the bike, I'll repay or compensate you somehow as long as you can get the bike to start running normally~
Thanks so much everyone~