I can't start up the bike -- HELP!

[7653]

I recently bought a used Suzuki GZ250 2002. It has 635 miles on the odometer.

During the sale the previous owner wasn't able to get the bike to turn over+fire up initially. He had to jump-start with a battery. Then he drove the bike around and it ran fine, at least according to my newbie observations.

When the previous owner transported and transferred ownership of the bike to me on a different day he said he charged up the battery for me prior. When we ran the bike it successfully turned over+fired up.

Since then I have tried multiple times to fire up the bike without success. When I press the starter button the bike goes gur gur gur gur (turn over) and the lights eventually start flickering and I hear whimpers from the bike. It doesn't fire up.

I checked the battery voltage it was at 12.1V. I called AAA road service to check it out. They said the battery just needed a jump-start after watching me unsuccessfully trying to turn over the bike. The starter button+jump start didn't work. Starter button+jump start+choke didn't work. The start button+jump start+choke+throttle did work. I left the bike running for 30 minutes and then I tried to turn over+fire up the bike again. It couldn't fire up while I pressed the start button/the bike was turning over. I checked the battery it was at 11.8V.

What is going on?
Do I need to buy a new battery?

Could the fuel in the carb have turned into jelly after being stationary for long periods? A local suzuki dealer ruled this out when I told him the previous owner drove the bike during the sale.

Any ideas or suggestions as to what I should do?