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?

It's almost certainly the carbs. You'll spend a _lot_ of money having
someone else do the job. Learn to do it yourself: it's not terribly
difficult, but takes patience, a clean workspace, more patience, tools
that fit the carbs perfectly, and even more patience.

Note that I said nothing about special skills, only patience. Krusty
Kritter/Kaybearjr/B-12 (same guy, different handles) has posted a carb
cleaning primer here many times over the years. Read it if you're
inclined to get the job done yourself.

Whoever does the work, once you _know_ that the carbs are clean and set
properly, you can go about checking for other problems if the bike
doesn't run right.