spark plug coil question

 I've got a 93 Suzuki Katana 750 that I am trying to get running.

When I bought it, it ran roughly, but you could ride it. Now, the only
way I can get it started is to spray a little carb cleaner in the
carbs. Then, it fires - but only runs with the throttle all the way
open.

My untrained ear thinks that it might only be firing on one or two
cylinders. Some of the spark plug wires from the coil are a little
deteriorated, but they look intact.

I tested each plug for spark, and although each did fire - I have a
hunch that one of the coils might not be providing enough power to
create a big enough spark to the remaining cylinders.

Does this make sense??

I understand that carbs on these older bikes are notoriously bad, and
I have just recently pulled them off. I plan to take the carbs to the
service department at the local dealership, as I don't know much about
how to rebuild carbs.

Any different ideas you guys might suggest at this point would be
great. Do you think I'm on the right track?

Thanks in advance.

-Joe

 Aside from the carbs (which, if you read this list for long, turn out to be
"the problem" more often than not), the "slightly deteriorated" plug wires
can leak much needed voltage. You could fire up the bike at night and look
at the sparks and corona around the wires, or just replace them on general
principles. Yes, there is a market for higher power bike coils for good
reason, but good wires with good connections minimize that need.