Cole is right don't take the car in in the state it is now. You can not drive three miles and expect the battery to be completely recharged. A battery charger is a good idea but not always practical a twenty minute drive will do it though. When you get the battery tested they will give you strange numbers which will be useless to the normal person. Your battery should have a minimum of 650 cold cranking amps (could go as high as 1000 for some batteries) if your only can supply 325 it is down to low to last a cold winter. So read the battery it will tell you what the amp capacity is on it. If your in that 1000CCA and down to 600 you should be good.

-Ask the person when was the last time they replaced the battery. If it's been more than 3 years. Maybe it's time again.

-make sure the battery terminals are tight, that each don't move by hand.

-Next look at Belts. Are they loose, frayed, have lots of cracks.

Fairly sure it's not the alternator because after the push start it kept running.

Yes. Your battery must be about to expire especially as it had an hour's drive to charge it. If you want reliability upgrade to a larger battery. Make sure it will fit the car and aim for high cold cranking amps (CCA).

Most places if your battery isnt charged will test it and say your battery is bad... of course if it isnt charged its going to test bad. Consider charging it with a 1-6amp charger before bringing it in. If it does fail i suggest getting a new one. They can also tell you the age and if its older than 4 years, id highly reccomend it.

GOOD place to start,............you can get a FREE battery check at Most parts stores

Ok 2nd hand Car I bought about a year ago.... Never had any problems before but today I came back from a 1 hour drive and went to pick up my kid at school.... waited in the car park with my engine off listening to the radio and had forgot to turn off my headlights for about 15 min.... the car just went Bgggg! and finally had to push start it

When I got home ( 3 miles) I cut the engine and restarted no problem....

Should I think about buying a new battery ?

thansk