You might want to try muratic acid,a wire brush,and a pressure washer.You don't need the pressure washer but it doesn't hurt,but a garden hose with a sprayer on it will also do.
Another thing is a floor sander,but im not sure as how this would leave the floor,so use a high grit sanding pad.
Use chemical gloves and saftey glasses when using the acid.

I feel that you will have to use lacquer thinner to remove the spray paint and be sure to have plenty of ventilation and turn off anu polit lights in the area. This will not damage the floor like the sander or the acid could.

The lacq,thinner may work too,but ive never had good luck with it,but I was using a little better paint than just spray paint.

Thank you both for the excellent suggestions. I'm glad to know it's not a hopeless case.

Mostly for archive purposes because I figure this guy has solved his problem by now, thinners (or muratic acids (?!?)) are mostly for cleaning WET paint or for recently dried paint. You need a stripper, not a thinner.

JASCO is a stripper product that I have used to completely strip everything (spilled wood stain, paint, carpet adhasive, ground in "stuff") in preparation for acid staining the concrete. It is amazing how it can strip concrete bare, even after years of wear. If it is ground in, you might end up with "ghost-like" spots, but spray paint should come off rather well.

There are also spray cans of anti-graffitti strippers available at home centers, as well.

I find this post funny, as I found myself in a similar situation - only I am the irresponsible son painting car parts in the garage and now I want to make it right for my Dad. I'm going to home depot and going to buy a wire brush, paint thinner, some graffiti remover...I will post back which worked best so we can close out this thread with a good answer of what worked.

So which worked best for you?

Hello everyone!

I'm Peter, and I'm new to the forum.

Wow, great tips on removing dry spray paint. I'll try one of the tips soon.

Peter Vekselman
http://www.biggerpockets.com/users/peterv

Wait, are you the guy who keeps removing my orange markings??