How do I charge the battery

If the battery is under the back seat like some models, charge battery.

When you accelerate the engine it rocks a bit under the hood. A loose/internally broken ground wire/cable under the hood is a possibility. Look for any and all wires/cables under the hood that might be loose. Wiggle all of these wires and don't forget any ground wires coming off the negative battery post. There are, I believe, ground wires at different areas under the hood. You might find your problem with one of these ground wires. The other possibility is at idle not a ton of charge is being generated from the charging system. Above idle an over charging voltage regulator can be the problem. It may be integrated into the PCM or be part of the alternator. A voltage charge test will reveal this. So, there are two possible sources of malfunction. Best of luck. And don't give up, you'll figure it out.

look rite under the steering column and there is a little handle pull down on it and the hood will pop.

remove belt and spend all pulleys. Inspect belt flat spots

look for main fuse panel under hood, there should be a charging circuit fuse check it

In the GL450 MB the battery is located under the front passenger seat. There are charging terminals under the hood on the right side. Look in the owners' manual under "Jump-Starting"

Batterys sometimes get sulfated and throw off any charge given them. replacing the battery is the first course I would take. Then check the alternator output. It should have a voltage of 13.0-13.8v for a normal charging battery. Internal voltage regulators are set to keep the battery charged when all the devices are being used. Check the large nut at the back of the alt to see what that voltage is. It holds the large cable to the battery to the output terminal of the alt. Then check the small wire terminal for power when the ignition switch is turned on. This activates the alt to turn on and charge the battery. Sometimes there is a mega fuse in the main fuse/relay center under the hood for the alt, check that also. Problem should be fixed now. I presume vou've already checked the cables are clean and not corroded to the battery, that will mess up everything all by itself.

Sometimes it helps to have a helper standing at the end of the hood, as you pull the hood release mechanism inside, have the helper pop the hood with palm of hand in area of release mechanism. I haven't looked to see if you could remove front grille?
If there is a national brand autostore in your community, they have been known to make house calls. Possibly, they could raise your hood, replace the battery or give it a charge, whatever. I don't know what they charge?
Sometimes you can charge your battery by hooking up battery charger to battery cable at your starter motor?

You say your test light was hooked from the negative terminal of the battery to the chassis? This is correct?
If so you don't have a short you have an open circuit.
You will have a bad ground somewhere between the battery and the engine or between the the engine and the body. Trace your grounds.
If you need more help leave a messege in "add comments" and I will help you along.

KL

I would check the altenator again. if you didnt disconnect the battery and a spark shot off while installing the new starter it could have decharged the spool on the inside of the altenator to where the spool no longer charges. if you have the altenator checked for consistant charging and it comes up good check the relay for the altenator it most like will have messed up the relay. to make a long solution short check the relay for the altenator it will be in the relay box under the hood.