The Dell E6500 service manual is here.
http://downloads.dell.com/manuals/all-products/esuprt_laptop/esuprt_latitude_laptop/latitude-e6500_service%20manual_en-us.pdf
Open up the laptop and check that the cable for the keyboard is firmly attached.
If it still acts up try replacing the keyboard altogether.
https://www.ebay.com/itm/GENUINE-Dell-Latitude-E6400-E6500-M2400-US-Backlit-KB-Keyboard-HT514/172929761919?hash=item28436ac27f:g:6ZcAAOSwcl1XPRPK