Your plasma television won't turn on. Maybe it has a blinking power or status LED. Maybe it turns on for a while and then stops working.
If you take your TV to a repair shop, it is very possible that you'll be quoted several hundred dollars to replace the entire power board. But all that may be required is to replace some bad capacitors.
Yes, you can likely repair your plasma television yourself for just a few dollars and an hour of your time.
To determine what's wrong, unplug your television and wait a while for the capacitors to discharge. Then open up the television and examine the power board. A blown capacitor will have a domed top from the expansion of the substance inside. Gasses push up through the top of the capacitor and blows out the top.
Once you locate the bad capacitors, note their polarity (which side is positive and which is negative) and remove them. Then shop either at a local electronics store or online to find replacements of similar or higher voltage rating.
See this video for an overview of how to find the bad capacitors in a plasma television power supply.