Black 2000 professional: need info please

I have a new condition Tag Heuer 2000 Quartz professional. I am going to put it out for sale and I need any information that you can supply me with. I am a watch novice. The watch looks like it has never been worn. I have provided a picture in this thread as I do not have the correct knowledge to describe it accurately. Thank you in advance.

Looks fake going on the screws on the dial. Think it's meant to be one of these: http://www.calibre11.com/wp-content/uploads/2011/03/Scans004.jpg

From my research today it looks like it is a 256.006-1. When you research this number it comes up. I have not found current value for this watch or the year of manufacture. Any help is welcomed. Thank you

It's in the 1985-1986 Catalogue on the Calibre11 main site Catalogs section, check it out here.
As your watch has the TAG Heuer logo, the -1 behind your model number 256.006 could be the reason for that, as the one in the picture is a Heuer. Anyways, very nice watch!
May be the description in the Catalogue might help you out with the sale:

Thank you, I wonder if this was made later than 84/85 due to the addition of Tag and the -1. Any suggestions on value.

85-86 would be the most likely timespan I think.
Any Heuer signed parts on it, like the bracelet, crown or the caseback-plate? If so, these are so-called "transitional" watches that were made after the merge from TAG with Heuer and sometimes they have used a mix up of parts, doesn't hurt the value much though.
Is the watch running, and running correctly? That would be a huge value point, as a service would set you back around USD 250 quickly (the chronograph module on top of the quartz movement is a pain to service) and parts are obsolete.

She has been sitting in a box since new, I have not taken back off too see if there is a battery in it. I am not going to service it. Should I attempt to install a new battery or would that do more harm than good if its not serviced at the same time.

Normally it couldn't do any harm as far as I can see it, but you will need a special tool for the caseback to remove, otherwise scratches on it are most likely. And if it does run, it will be probably full with old oil/ grease that has gone bad and is now like as hard as chewing gum, so the chance it is running fine is most likely not that high.
I would leave it alone, keep it closed, advertise in the state it is in complete with all the possible items you have with it (extra links, box, receipts etc.) make excellent pictures and a good description, the buyer can then do whatever they want with it.
I would conservatively value it in this condition at around USD 450-500 because of its nice outside N.O.S. condition.
See it as a great opportunity for a watch-collector to repair or for parts.
But running and serviced at least USD 750+.
Hope the info helps.

Yes, thank you. I may list it on here when the time comes.