WIthout more information, such as source, and connected equipment, it's difficult to troubleshoot, but you can start with the basics.
1. For the TV itself.
a. make sure all connection cables are secured on your source components, as well as the back of the TV. Make sure no cables have been cut, or severly damaged (run over with a vacuum, or the like).
b. When a plasma tv is powered on, you may be able to see some tiny red green and blue colored dots in the screen if you take a closer look at the panel(with your face a few inches from the screen). If you do see activity, your screen is probably powered, and you might have an input issue. If it is completely black, with no color, or movement whatever, the panel probably is not getting power.
c. The last option for your TV could be a picture off mode for listening to music. My pioneer elilte has this mode, and it is pretty easy to completely turn the picture off. You should consult your manual for this.
d. Edit. Try changing the input on your set, It's possible you only have the issue with a single source.
2. For the remote, if you have supplied fresh batteries, you can easily test any infared remote by pointing it at the lens of a digital camera, or camcorder with an LCD screen. If the remote is operational, you will see a white flash in the LCD when you press a button.
Aside from the basics, you should consider contacting your local repair shop.