How safe is an ungrounded outlet?
So I just moved into an old townhouse (renting)... I've been unpacking my things and I plugged my TV and assorted gadgets (Roku, DVD player, Wii, etc) into a surge protector.
I noticed the surge protector had a red light that lit up indicating the outlet (while being three prongs) is ungrounded. I tested it in a couple outlets around the home, and it appears the outlets in the kitchen and for AC units are grounded, just not others.
What risks would I run plugging these items into this? Electrocution? Item destruction?
Also, the place where I'm putting the desktop only has a 2-pronged plug... I know items called "cheater" plugs exist to allow plugging a 3-prong device into a 2-pronged outlet. What risks does this pose, of any? Of course I'd used a surge protector as well.
Should I be hiring an electrician (or talking to the landlord) about rewiring the plugs? Or perhaps installing GFI outlets?
Any advice is appreciated, the things that pop up in a Google search are pretty sketchy.