Light on dash reads "check

No. Charging voltage should be above 13 to 15. BUT, this vehicle has GM's power management feature. It only charges when it needs it. Read this post to see how it works. Ask the shop if they conducted the proper tests for this system.

http://ricksfreeautorepairadvice.com/gm-charging-system-problems/

you have to drive it to charge the battery back up or put it on a charger

Year make and model, and do you mean volts instead of amps ?
Will the battery stay charged if you disconnect it overnight ?

When you replaced battery you activated the system. Need to read owner manual and see if it tells how to deactivate it. You may need to contact dealer to deactivate it.

It wouldn't be the starter. It will not draw current when not engaged. Could be a light left on, a trunk light, glove box light, under hood light-an unintended drain, somewhere. Sometimes a penny or something gets stuck in cigar lighter and keeps that circuit on.
You should check if alternator is fully charging up the battery after it has run, and then turned off. But if you don't have a voltmeter handy, try this: When you shut if off to sit overnight, take the negative battery terminal off the battery. When you get ready to start it, hook up the battery and see if battery is no longer weak. If battery is now good, you do have an unintended drain. If battery is weak again, check charging system, battery cables and connections, alternator connections-a loose connection will prevent battery from charging.
If you have a drain, turn everything off and remove key. Pull the bulb out for the underhood light. Take negative off battery again, and hook up a testlight between the negative battery cable terminal and the negative battery post. If something is pulling current, the testlight should be bright. Now at fuse panel under dash, pull fuses one at a time and watch the testlight. If you pull a fuse and the testlight goes off, that circuit has the unintended drain. Check everything on that circuit.
Hope you find the problem. Good luck.

Sound like a problem with the oil sending unit or ground wires connections, that drain your charge overnight. Check it to solved.

HAVE VECHICLE CODE SCAN.SEE WHAT CHECK ENGINE LIGHT CODE YOU ARE GETTING.

Well contact your dealer and tell them that your battery is gone bad for no reason and don't mention you let the light overnight because your battery is under warranty and they will put in a new one. Good luck

If you have a fuse it will be in the power distribution center near the battery main fuses and relays are inside.
Check the charging system with a volt meter right at the battery. Battery standing charge should be no lower than 12v if charging you should read between 13 and 14 volts running, about 13 with all electricals turned on. If not, the alternator isn't working OR the regulator has failed. (some regulators are part of the main computer but you need to check which system you have. AND do check for fuses.
If charging system is working you may have a system draw that is pulling the system down overnight. Check that with an ammeter between either cable (removed from battery) and battery connection...pull fuses one by one till draw disappears then check components in that system. Don't be concerned with "low Draw" items such as radio that always pulls something to keep memory and clock working.

It could mean the alternator has gone bad already... with the car off, the battery leads should read 11-12V.. with the car on, the battery should read 13-14V.. if it's lower then it's not charging your battery and if it's higher, it's damaging your battery....