Why did my 2006 saturn ion not want to exelerate after a battery symbol with an arrow pointing downward showed up on the dashboard

Do you see the little pad lock symbols and the arrows pointing out? Those are the release clips.

I would be checking the drive belt tension
then I would be checking battery terminals for tight and clean
then i would have the alternator and regulator bench tested
Also I would have a load test done on the battery
The performance from the engine , probably resulted from below required voltage to drive the ECM and electronic components , which indicates what I have suggested to check

There is most likely a problem with your charging system. Modern cars are very dependent on proper electrical power flow. If your charging system is not working correctly your engine will not run well, and eventually will stop altogether.

if your car has a standard transmission then the icon of the engine that has arrow pointing down might be an indicator that you need to down shift , as

the other symbol ive seen only once before it was on a Bmw and was a symbol for the valet mode , it down tunes the engine and inhibits all the luxury features (like radio) for just the valet to park your car , its possible these two icons are related

It sounds like you are describing a water temperature warning light.

This sounds like a reset problem. Possibly the ignition interlock ( Just another word for Factory reset code needed for your computer.) Usually the little padlock symbol will be on in dash. Removal of the battery could and usually will fool the computer into thinking the car is being hot wired into starting.

CHECK COOLANT LEVEL IN COOLANT EXPANSION TANK.SOUND LIKE LOW COOLANT WARNING LIGHT.

Hello, That symbol indicates low coolant in the radiator.

try www.edmonds.com for owners manuals online

passlock symbol.... The ignition switch is faulty... very common on the ion 2003 to 2006.... new design switch in 07