Tractor Repair: Case 1070 Tractor starting problem, solenoid starter, battery cables

Question
Hello Arnie, I have a recent problem with my 1070 Case Tractor 5700 hrs. Tractor has been very reliable. Plugged in in the winter it starts with ease. I started it yesterday to do chores, while  I was out in the field i shut off the tractor while I was hunting gophers. When I went to restart approx. 1/2 hr later it did not start. I used my truck to attempt boosting. Tractor turned over very briefly and slowly then quit. Left truck charge and also hooked up battery charger. Tractor would only turn over briefly approx. 3 secs. and died out again. Pull start tractor with truck. Started instantly. Ran tractor approx. 1600rpm. 40min. Cooled down shut off. No restart. Dead again. Put battery charger on overnight at 12V 40amp. Attempted to start this am. Dead at key.Turned charger up to 200amp boost. Clicking was evident but no turn over. Condition of battery is older but has only required one charge this winter during an extreme cold snap -38c. Cables are older. Question: Before randomly replacing parts, battery, cables, solenoid, starter bendix drive etc. Do you know where I should continue my investigating. I have attempted to check if connections are loose, everything appears tight. Any advice you could give would be appreciated greatly. Thankyou, Terry.  P.S. My mechanical knowledge is somewhat limited but I am capable of fixing a problem if I am confident I am on the right path.

Answer
  If the batteries are more than 5 years old, I can guarantee that they will need to be replaced.  First remove the cables from the battery posts and clean everything until it's shiny.  If there is any corrosion, it will need to be cleaned and if the clamps are eaten away, cracked, or the bolts can't be tightened, replace them.  Make sure there is a good connection where the negative cable grounds to the tractor.  Make sure the starter connection is clean and tight.  To accurately test the batteries, they should be tested with a load tester.  I would suggest taking them to a repair shop or auto parts store that can load test them for you.  If a battery is bad, no amount of charging will help and usually you can't even jump start them.  Jump starting only works if the battery is dead but still good otherwise.  With a voltmeter, check that the alternator is charging OK.  With good charged batteries, it should charge about 13.6 volts.  I doubt that it is a starter problem, but nothing is impossible.  Turn on the lights and see if they are dim or if they go out when you try to start it.  If the lights are OK, then it is a starter problem.  If the lights are very dim or if they go out when you try to start it, then the starter is OK and it is a battery or connection problem.