Ground wire is hot, drop ceiling carrying current?
It sounds like there's an ungrounded (hot) conductor shorted to ground somewhere. Finding the short is likely going to be a tedious task.
Check your work
Did you install grommets or clamps, where the wiring passed through knockout holes in boxes? If not, start by inspecting the wiring where it passes through the knockouts. The edges of these holes (especially on thin recessed lighting boxes) can be quite sharp, and can easily damage cables and wires as they pass through the hole.
Check all your connections, making sure nothing came into contact with ground or non-current carrying metal. This can sometimes happen when wires are pushed into boxes, so check for loose or pulled out wires.
Inspect cables/wires where they are supported, especially where supported by metal staples or clips.
Check existing work
Start by turning off each breaker in the panel one at a time, while monitoring the voltage on the drop ceiling rails with your non-contact voltage tester. When the voltage goes away, you've found the offending circuit.
Once you know which circuit is causing the problem, it's time to start the tedious task of locating the fault.  Do your best to trace out the circuit, and determine all the equipment on it.  Open up all outlets and equipment, and inspect the wiring inside.
It may help to move along the circuit, and disconnect the load conductors (the conductors feeding the next junction) at each junction. Then energize the circuit, and check for the voltage again.  This can help you isolate the problem, and will help you focus on the problem wiring. Once you find the offending part of the circuit, methodically inspect the wiring. Checking for damaged wiring, loose connections, improper wiring, etc.
Unless you get really lucky, you're likely in for a long tedious search. Good luck.