Hello psnewman.
The Pulsar experts of this forum will probably give you more specific help, but first i'd say get some batteries in the watch. If you are going sell the watch on a website like ebay.com, it will always sell for more if it is confirmed working. Unfortunately, if it has a dedication engraved on it, this may emphasise the sentimental value, but will almost always result in a lower price than a non-personalised item.
If you search for 'LED' in ebay's buy section, specifying the 'jewlery & watches' category, you'll get an idea of what pulsar LED watches sell for. You might sell to a online vintage watch website, but your likely to get less, because the buyer will have a significant mark up, to make a profit, but still has to price the watch acccording to market forces.
A few hundred dollars is very possible through ebay, depending on circumstances (i.e. working, and not personalised) Good luck.