Wait... are we saying that this English car may have a ground issue 
While you are looking at the grounds, make sure the block / drivetrain ground well to the frame and the battery ground is good (is it under the back storage area like the MGBs?).
And hey, look at it this way, once you get it running, it will be FULLY tuned up (you pretty much went through everything!)
Yea, shocking, a 53 year old english car with a sudden and mysterious electrical problem, who would have thought!
Today I picked up a new coil to be sure that my used spare was OK, and ordered a condenser as nobody local had one in stock, but it will be here tomorrow at the NAPA down the street so I can put it in in the morning and if it works, I'll still make it to the car show tomorrow.
Sonic wrote: I triple checked the points gap, and cleaned them with a nail file, the points look new (which they basically are).
The nail file is a bad idea. Points tend to have a very thin platinum coating on them. I assure you the nail file has removed that.
Try a new set of points and a condenser.
Another thing to investigate is the rotor. With the cap off and the key on, spin it over while holding the coil wire (the one that goes into the cap) near the spinning rotor. If you see a spark, the rotor is grounding to the center shaft and is toast. Had two rotors in a row drive me nuts with this problem; both new rotors.
The ignition system on my MGA is why I moved it to a pertronix electronic. It all hides in the distributor and works very well. Might be worth looking into for the future. I also added a single Weber carb and eliminated the two reasons I sat on the roadside in the old Austin Healey.
Yeah I would look at Pertronix. They aren't expensive at all.
I have a Pertronix in the Rolls Royce, it's great, and I agree it is a long term solution here, right now I'm just trying to get it running for tomorrow.
Sonic wrote: I have a Pertronix in the Rolls Royce, it's great, and I agree it is a long term solution here, right now I'm just trying to get it running for tomorrow.
Isn't there a build thread for the Rolls?
Check fuel pump output. They will still click away but can be supplying way too little fuel.
Pertronix was the best add-on I did to my Opel GT. The original coil went out and when I bought the replacement I bought the whole kit, Flamethrower coil w/Pertronix electronic. Once I got it working, had issue with no resistance wire in ignition so had to add a ballast resistor, the car had never ran so well and had as much power since I've had the car running.
By the way, when the coil went out the symptoms were similar to what you have but you stated you changed it so I stayed out of it.
Another update!
Replaced the coil and condenser, went to start it and...
Nothing. 
Still no spark. Nothing on the plug when pulled, and nothing on the timing light. I checked the ground path, it looks fine. Dammit. So, at the car show today we brought the Rolls instead of the MGA, which was still fun. Lots of people think that a beater Rolls Royce with a roll cage is lots more interesting than muscle cars in every skittles color
So now I'm ordering a Pertronix to replace the points and we'll see how that does, as the points are the only thing I haven't replaced in the ignition system lately. I"ll keep you updated, thanks for all of the suggestions.
I remember trying to replace the points in my Sunbeam, way back when.
there was a fiber washer the got left out of the "build" ... no fire .. nothing ... took a long long time to a: find the washer ( I didn't know I was looking for it ) and b: figure out where it went ... after that ...cake
You've got something unhooked or shorted out.
Update!
I got the Pertronix ignitor in the mail today, one day earlier than expected. Thanks, Amazon.
As usual, these are a quick and easy installation. I got it put all back together, hit the starter and....
No start. Dammit.
I keep thinking through what I did and the path of the spark, and then realize, I forgot to put the rotor back on when I put the ignitor on! So I put the rotor on, then engage the starter from the engine bay and....
Started right up and ran great! I didn't get to take it out for a real road test tonight as it is blocked in by two other cars, but from letting it idle and rev up in the garage, it is running far better than it had been before in these conditions. Tomorrow I'll get it out on the road and give it an italian tune up to blow all the crap out from trying to start it so much this last week, then fine tune the carbs a little.
Thanks to everyone for all of the help! 
Put the rotor in your mouth, when you dry it off check for cracks
I had the same issue with an MGB: tuned it up, had it running great and then put it away for a few months. After I started driving it again, it ran bad like your MGA. Take the carbs off, clean the fuel bowls completely, check the fuel jet and needle for fuel varnish, new fuel filter, remove all the fuel from the tank (use fuel pump to drain some of the fuel, it will flush the lines too) and replace the fuel.
You probably have some sediment or gummed up fuel in the tank/lines/carb. Lastly, check your spark plugs. If it's been sputtering and running inconsistent, it may have fouled the plugs too.
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