I experienced hand numbness after riding in the drops for long periods and found out it was caused by excessive pressure of the bars against my hands because of inadequate reach. With a 20mm longer stem I became more comfortable but ended up with a 30mm longer stem because I really liked the stretched out position better. Anything less than about 15mm change in stem length is almost unnoticable to me.
I'm uncertain how a longer stem might affect your neck pain. It seems possible to me that a longer reach and lower stem could help transfer more weight onto your pedals and core muscles instead of your arms and as a side effect reduce tension in your shoulder area and neck. By using a stem calculator like this
http://www.yojimg.net/bike/web_tools/stem.php and by searching ebay for alternative suitable stems you could experiment. If you're uncertain about the variations of component sizes I recommend buying a caliper like this one to measure parts:
http://www.harborfreight.com/6-inch-...iper-7914.html Be forewarned that some sellers on ebay unintentionally misidentify stem measurements.