Slow engine turnover, then

i have 2003 pontiac grand am.

the car drove just fine yesterday (early evening), but then the next evening when i went to start, the engine failed to turn over.

Left the car alone for 1-2 minutes, then tried to start again.

this time the engine, very slowly and laboured, turned over but again failed to start.

Tried again and the engine increased its turnover rate steadily as I kept the key turn, but still labored and still no start.

any help would be great.

thank you

Take your pick:

Low or near dead battery
Corroded and/or loose battery cable connections
Bad grounds
Faulty starter or starter solenoid.
Fuel fault or no spark

More info needed from your end. (ie., age of battery, recent work done, etc.)

no major repairs on the car.
it has about 62000 miles on it.
i replaced the battery a couple of years ago.

interestingly, after my first posted message, i tried again and the engine started right away.
i drove it around the block, just in case it lost a charge, and then turned it off.
i started it after a couple of minutes of letting it sit and it started up again.
then, i let it sit for about an hour and went to start it…it started on the first turnover, but the first turnover seemed rougher than normal.
thoughts??
thanks for your help.