Sorry, I got interrupted yesterday. The first thing to do is buy an outlet tester at a hardware store. See if that also indicates bad ground. I had a UPS (uninterruptable power supply) that had a light that indicated bad grounding, but I ran the circuit and knew the ground was good.
If the outlet tester also indicates bad ground, then you have to start tracing the lines. The "easiest" thing to do is determine what's on that circuit and then attempt to follow the circuit from the breaker box to the end of the circuit. For outlets, they sell a device that you plug into the outlet and then you take a separate device and run it over the breakers, and it tells you which breaker corresponds to the outlet. For lights, you just have to turn off breakers one by one and see what goes off.
Anyway, this will allow you to determine what's on that circuit. Then you go into every switch/outlet box to see if the ground is properly connected. The grounds should be connected in each box (that is, the wires that "pass through" the box should be connected together, in general, hot to hot, neutral to neutral, ground to ground) and to each switch (well, my house was wired without grounds to light switches, but perhaps that was code at one time) and to each outlet.
As for whether the surge suppressor would not work, my guess is that it would not work correctly without the ground.