Volt light i have the same problem. will a new battery get the car to start?

Get a different alternator. 13.5 volts is too low. It needs to be 14 to 14.5 volts. The other battery is over charged.

The BATTERY light indicates that your battery is not getting charged. There could be several reasons for this most probably your alternator, which generates the current to charge the battery when the engine is running. If the new battery is not getting charged, it will eventually drain not start your car. To confirm that the battery is not getting charged and that is the reason for the BATTERY light, put a volt meter across the battery while the engine is running. It should read around 13 volts indicating that current is flowing into the battery. If it reads 11 volts or less, that means the batter is being drained and not charged. Then have your alternator checked.G

The problem is more than likely a dead cell in the battery, Each cell in a battery is normally 2.3 volts, they will go over but when rested will return to 2.3 volts, with 6 cells it is 13.8 volts, car starts. 5 good cell is 11.5 volts, almost enough to start, any less not a chance, the starter will just click, cold weather is worse. A new battery will solve the problem

The Battery CCA Rating is to turn over the starter

CCA--Cold Cranking Amps
That is at zero degrees
Total cranking amps is at 32 degrees

The car runs off the alternator
It puts out over 14 volts

The 12 volt battery is 6 cells @1.2 v each = 13.2 v

You need 12.6 volts to test a car or you charge it first

You need over 13 volts to charge a battery,thus the alternator

The only other job the battery has is a stabilizer in the electrical
circuit

So you need to have the charging system diagnosed as the
various light you have on should be off when engine first starts

First put your battery on a slow charge 6-8 hrs.then check the batteries voltage it should have at least 12-12.8 volts if it does'nt then you need a new battery.If has 12 volts after its charged and goes dead after its installed in the car then you need a new alternato.

First check for spark at any of the spark plugs.

Generally if charge light is on, alternator has a bad diode in it. This lets the charged battery lose its power by flowing in the reverse direction. It sounds as the alt., is either not connected right or is swtill bad

try shifting it to neutral then see if it will start if it does then you have a bad gear position switch if not could be a bad starter or ignition switch

maybe the alternator