Is it a battery problem or starter??

Respectable on all levels.

Go talk to the parts houses though and they'll be more than helpful to walk you through this stuff.

 

If it's holding 12.7V then it must be a starter issue like the brushes or a poor electrical connection. But it wouldn't hurt to check the battery cells and clean up the connections. Have someone help you crank it while it's cold and dark outside and see if you see any sparks at the solenoid. I've seen the main hot at the starter solenoid do that before. It didn't take a 1/16th of a turn to fix it.

 

If you can get to a PARTS SOURCE store ( owned by Canadia Tire ) they will do a load test on your batteries at no charge

 

If what you're saying is true , and I don't doubt it is , you have weak batteries. It may only be one , but , look to replace all of them. If you want to try to get through the summer with them, buy a good set of Long jumper cables. At least 4 gauge. You didn't say what part of the country you're in , or even what country , but I'll tell you , hot weather can kill a weak battery ,just as quickly as cold weather.
Good Luck !

 

You didn't say what part of the country you're in ,or even what country his location shows Toronto Ont that is in Canada

 

parts stores DON'T know how to test batteries. NOR do they have the proper equipment.

anyone can test a battery with a 50 amp machine. even a 9 volt duracell will pass the test.

you need to pull 500 amps to properly test the batteries.

i explained the test procedure. NO parts stores follow that procedure.