Linoleum floors are designed to be long-wearing and take substantial abuse, in addition to these wonderful attributes it is also very cost-effective (as far as floor covering goes). If the damage/wear is really bad consider replacing the linoleum, it may be much less headache than attempting to clean a surface which is degraded beyond rejuvenation. Only you can answer that question as we have no idea how large and area and what the damage is. Also, since it's your business floor you might be able to expense the cost of a new floor, not sure if cleaning classifies. Good luck.
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Try using a floor polisher and a rough pad. You can rent these at hardware stores (like home depot) and even some large supermarkets. You may need to use a cleaner of some sort along with the polisher - which cleaner you use may depend on what's stuck to the floor. You could also hire a cleaning company to do it for you.
A commercial degreaser or wax stripper with the use of a machine scrubber with a rough pad should do the job. Just make sure to rinse the floor very good. You may use a wet vac to suck up the excess solution from the floor. If not I recommend replacing the floor.
If all else fails, I suppose one could always apply a good coat of floor paint. I believe there was an 'ible which suggested that if you want something more decorative and durable, you can seal paint under a coat of polyurethane floor varnish.
. Use a floor buffer with a "scratchy pad" on the bottom. This will get rid of all the old wax and dirt and most of the minor scratches. Wax when it's clean enough for ya.
Go aggressive: Diluted caustic-soda, like 5%w/v use protective gloves etc. Brush. That's me, no disclaimers otherwise. L
There are aggresive industrial floor cleaners that might help. Try a good janitorial supply company. Once you've cleaned the crud off, you can then float on a nice new wax layer.