'88 300SEL No tranny fluid...How much damage???

I got a call from my daughter yesterday that the car, a 1988 300SEL, wasn't shifting properly. So I tell her to check the transmission fluid level and it turns out there was almost no fluid in the tranny.
She goes and buys 4 quarts and puts them all in. Fluid level is just a little above marks now.
She tries to drive it and it still won't shift properly. She says it revv's really high, up around 5K, and won't shift. And when it does the whole car surges forward.
She said she was doing around 45mph at 5K revs and it wouldn't shift.

What could be causing this problem? Could the tranny be damaged? Is the pump trashed or could it just be the modulator? Or maybe the fluid just needs to flow through for a little while?
I'm just grasping here. she really needs the car for work and school and I don't know how to fix the shifting issue.

Also, probably not related but when I drove it it ran fine except for a shimmy from up front at high speed. You could hardly feel it below 45 or 50 mph. I thought it was from the tires since they are old and need to be replaced. or maybe a warped rotor? I haven't had a chance to look at this, she was going to bring the car over this weekend for tires and some DIY maintenance.

Danny

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1984 300SD Turbo Diesel 150,000 miles

OBK member #23

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