Lol...finally a question on ssnakess right up my alley!!! Guess what i do for a living
Okay...so your battery was toast..and the caa guy probably mis-directed you into buying a new one which lead you to replacing the alternator that was the problem in the first place. Ive been there...one of those guys tried to sell me a battery in september...then told me that my alternator was not charging as well....after i informed him that i was a mechanic and then showed him how to read the meter i then declined to buy anything from him...guess what..same battery, same alternator, still everything working....needless to say he was quite embarrassed at the fact that he didn't know how to read the meter properly.
Okay...to make a car run...with or without electronics...here is a brief over view. You need all of these three things...unless its a diesel..you can eliminate one
You need, fuel, air, and some way to burn it...aka spark. Get rid of all your electronics and everycar still pretty much works the same way. Here is what i would do. I would charge the car again. Make sure if you have a multimeter available to monitor what the battery voltage is while charging...get as close to 12.6 volts as possible. If you dont have a battery charger, turn the key forward and monitor the onboard gauge. Your car should have at least a voltmeter of some sort on the dash. Let the car charge for awhile. You may have pulled the battery down to near zero voltage which will cause the car to not have enough power to turn the starter. You stated that you only got one or two revolutions from the starter. This tells me that you either didn't charge it long enough...or you didnt have proper connection of the booster cables at the batteries...lights or no lights, it takes amperage and lots of it to boost a car. If you try this and it still doesnt work, i would then disconnect the cables and see if you have fuel. Keep the cables off for fire prevention
If its a carburated car...take the air breather off and pull the throttle back..you should see a little stream of fuel going into the carb. If its fuel injected or throttle body, look for the fuel rail around the intake. There should be a test port that looks like a tires air valve. Gently push the centre in with a screw driver...and make sure its gentle..dont break this lol. Have someone crank the car over. If fuel comes out your good...if it doesnt...you need a fuel pump...but i doubt you will have to go this far.
Lets back up a bit before i run off and confuse even myself. Okay..so there is a new battery, there is a new alternator, and there is a starter that barely turns. Lets say for the fun of it, that you actually did boost the car right. Lets say that you installed the new parts..but either a) didnt disconnect the battery while installing it, or B) you might have touched a positive cable to ground. Look at all of your connections. Make sure everything is tight wire wise. Follow some of the wiring to make sure they are not melted. Most vehicles charge wire runs off the alternator directly to the starter..which then runs to the battery. They are three in the same sometimes. Isolate these first, if everything is 100% and your confident its 100% then move onto fuel. If everything is good there...your probably getting a problem with a computer sensor...ie a crank or cam sensor...neither of which is able to pick up top dead centre anymore......but thats a whole new lesson.
Start back at the basics...boost, let it charge while boosting for a bit..then start into wiring etc. Let us know how it goes
Hope this didnt confuse you more