When, my girlfriends mom gave it they had just tried to put a new battery in and wired it backwards (not entirely their fault I guess, cause for some reason the ground wire has a red band). Anyway, it friend the wiring harness, they got fed up with it and gave the bike to me for free, so im not complaining. But I am sure the battery isnt in great condition becasue of this. But I figured that as long as it started up then the electrical system and wiring was fine? I just assumed this wasnt going to affect it dying.
Well, until you told us this, I would have thought your carburetor slow jets were clogged. Although they still might be...
Reversing the battery connection almost certainly damaged the rectifier in the charging system, and likely some of the wiring and connectors need to be replaced. I'm guessing you can't electric start the bike either because the battery is poorly charged.
To have spark you need voltage. During start this is supplied by the battery.
Your alternator may be producing some power through the undamaged portion of the rectifier. But, it only makes enough power to overcome the electrical load of the lighting, coils and alternator field, when the engine is revving up. When the RPM falls below that threshold, the battery voltage falls from depletion, the coils can't make spark for the motor and it dies, sometimes just as you apply the brakelight.
If you just want to drive around the block, then get yourself an AUTOMATIC charger/tender. Unless you are committed to learn a lot more about things electrical, avoid the cheap trickle charger, especially ones for automotive use. IF you don't personally monitor the use of trickle chargers, you'll be buying new batteries frequently.
Charge the battery, don't use the lighting, and you may be able to drive around the block.
If you want to see if your charging system is functioning for longer trips, then get your self a digital multimeter. They can be had for under $10, and with your bike's history you're going to need this.
With it, measure the battery voltage. Start the bike, And measure the battery voltage again at 5000, 4000, 3000, 2000, and 1000 RPM if it will idle.
Write down the numbers and do the test again with the lighting switch on.
Tell us the numbers.
Carbs:
One has to wonder why the carbs were rebuilt last year? And, if the cause may have been fuel contamination.
The 74 CB550 has a sediment bowl at the bottom of the petcock. It unscrews (lefty loosey) and in it you'll find a sampling of what the carburetor may have been fed. If you feed clean carbs dirty fuel, they become dirty all over again.
Also in the petcock is supposed to be a fuel screen to block that stuff you found in the petcock bowl. Remove it with care and check it for holes clean the bowl and the screen and reassemble.
If you found anything other than pure fuel in the petcock bowl. Ask yourself where that came from?
Why, the tank, of course. So, look inside the tank and see if there is dirt or other contamination like rust inside the tank.
The carburetor slow jets supply fuel at idle throttle settings, and meter fuel though an orifice that is 0.016 inches in diameter. Clean fuel molecules are considerably small than this, but lumps of debris from the fuel tank won't and will block the fuel from getting to the engine, making clean carbs in instant need of cleaning.
There are four carbs and four opportunities for fuel blockage. If your throttle is at or near idle, the exhaust head pipes will be cold(er) on cylinders with blocked slow or idle jet orifices.
You are likely going to need a Shop manual to rescue the machine.
Good luck!
