A 12.34 volts at no load reading indicates a completely discharged battery. You should have 12.6V, or ideally 12.9V right after charging.
It sounds like it could be low battery along with flooding due to very short runs in the cold and slow starter. When you get a good battery, you may need to hold the pedal to the floor to clear the flood at first.
You spray staring fluid into the air intake on the air filter box.
OK so I'll start this post with a little ditty that is also a clue to what I found this morning though there' still a puzzle:
Joegr, Joegr he's the man
If he cant fix it no one can.
So here's the detailed story and the puzzle. Preface with I have 3 LSes, all 1st Gen. 2 are now running:
Car 1: 2001 Gray, 120,000 or so miles. My daughter has been driving this. It is the car that would not start on Thursday. The battery in it was a genuine Ford made for LS with gas drain hose. It advertised on the label "750 cold cranking amps". I read that the LS battery has 650 cranking amps but I figured an extra 100 wont do any harm. I remember buying this battery shortly after I purchased the car which was around November of 2015. The battery has a little sticker on it says 4/14. Seems likely to be mfg date.
Car 2: 2000 Silver, 199,000 miles. I've been mostly driving this one. It had sat in my cold storage workshop on jack stands for about 6 weeks. When I went to check it on Thurs it started quickly but initial cranking was a little slow. The battery in it looks exactly like the other battery but says "650 cold cranking amps". I took it off the stands and have been driving it last couple days while daughter driving my 2004 Navigator which she loves except for the gas mileage.
OK so I'll get to the point: I swapped the batteries this AM. I put the 650 Amp battery in Car 1. It cranked well, kicked over for a second and stalled again. I put the pedal to the floor and turned the key again and voila it started right up! (I never knew about the pedal to the floor clearing a flooding condition.) While in there I turned the Innova loose and it again said battery voltage low (about 12.0 volts.) Then I ran the alternator test and Innova said that was working fine. Good.
Then I took the 750 amp battery which would not start car 1 and put it in car 2. Started right up. Ran battery test - voltage too low about 12 again. Alternator test ran fine.
So why would the 750 amp newer battery die first? Why would it start one car and not the other? Could it be that car 1 was flooded the whole time and I never cleared it? I am going to put the 750 amp battery back in car 1 after attacking the posts and connectors with some emery cloth. I will report back with a much shorter post. I am wondering if I should return one of the batteries? Take it to Ford and ask for exchange which the label says free within 3 years. They could do a load test to convince themselves it's out of juice.