Do I need a new coil? Does brand matter?

[ILENGINE]

Model type trim code
445677 0827 E1 071005YG

The code is the date of manufacture in this case October 5 of 2007 and the last two letters are factory manufacture codes.

The model, type/trim are used for parts lookup and in some cases the code if more than one part was used with different dates. The word trim isn't normally stamps into the part. Normally just stamped with the words model, type and code similar to how I listed it at the beginning.

 

[Rivets]

If this unit came in with this problem I would probably start by checking over the fuel system for air leaks. Things I would be looking for are leaking gaskets and cracked intake manifold. To check I would take my can of carb cleaner and with the engine running I would spray any area where the fuel would travel from the carb to the engine block. To do this you will need to remove the shroud to access the manifold. You can run the engine for a short period of time, at low speed, without worrying about over heating. If the engine speed changes you will have found an area where air is entering. If no changes then I would be looking at cleaning and rebuilding the carb. Note, these carbs are not the easiest for the DYI to do, so take a close look and this manual before you decide to tackle. https://docs.google.com/open?id=0B6NaqjIxWV1ySkZjTTA5TGltZEE

 

[tluxtele]

If this unit came in with this problem I would probably start by checking over the fuel system for air leaks. Things I would be looking for are leaking gaskets and cracked intake manifold. To check I would take my can of carb cleaner and with the engine running I would spray any area where the fuel would travel from the carb to the engine block. To do this you will need to remove the shroud to access the manifold. You can run the engine for a short period of time, at low speed, without worrying about over heating. If the engine speed changes you will have found an area where air is entering. If no changes then I would be looking at cleaning and rebuilding the carb. Note, these carbs are not the easiest for the DYI to do, so take a close look and this manual before you decide to tackle. https://docs.google.com/open?id=0B6NaqjIxWV1ySkZjTTA5TGltZEE

I'll check this when I get a chance as well.

I know this is a ways down the road... but let's say it's the carburetor. How long does it take for the average person to rebuild it? Aware of any good tutorials on youtube? I'm guessing the parts wouldn't be that expensive.
Now let's say I don't have the time to rebuild the carb myself. Would you suggest taking it somewhere (if so, where do I begin to look) or simply buying a new one? What would I be looking at cost wise?

 

[Rivets]

U-tube, I have no ideas, as I very, very, seldom go there. Average person rebuild, if you’ve worked on carbs 1 1/2 hrs, if you’ve never worked on carb I suggest don’t even try. This will not be cheap, kit $90.00, labor minimum of 1 hour after the carb is off. Cost of carb approximately $200.00. I would suggest that you find a repair shop with the oldest, experienced mechanic in your area and have him troubleshoot the problem. Yes it can be expensive that way, but with this type of problem it may be cheaper in the long run. Remember here we can only give advice based on our experience and what you tell us. We are not standing next to you to experience the problem, so what we say could very easily be totally wrong and we could send you down a $$$$ path. Read my signature before you proceed

 

[bertsmobile1]

Similar to what Rivets has posted.
Being that your problem went away when you removed one of the kill wires suggests that the problem is in the wiring .
So if your mower has a carburettor solenoid, check that it is working
If so the remove the kill wires from both coils ad go mow
If the mower runs fine the kill wire is your problem
On some B & S twins there is a diode in the wire that connects the coils.
This prevents the coils interfearing with each other.
Search "Kill Diode" on this forum for detailed instructions for replacing it with a standard Radio Shack ( they still around ) diode or spending a bit more & getting the Briggs repair kit.