All electronics are subject to burning out, catching fire and all TV's are subject to getting dull. So your dad is sort of right. The correct question is what types last longest.
Plasma TVs are subject to burn in, not burn out. The newer sets are supposed to be better than the old sets. I have not seen any personal testimony to that effect yet but I have seen some of the original plasma sets after 1 year where the playboy bunny or SCiFi is visible in the lower left corner no matter what channel is currently selected. The plasma screen itself tends to remember what was displayed and after a while the image quality degrades as old images cloud the new. Plasma lasts a lot less time than a CRT lasts. We're talking 1-2 maybe 3 years VS 10-15 on a CRT TV set before the image becomes unacceptable. There is no economical fix for a Plasma screen. There used to be a trick to re-energize the CRT electron guns but it is not worth the cost anymore.
LCD, Projection, DLP and CRT (the classic picture tube) are all subject to wearing out. The first 3 use (expensive) high intensity light bulbs for projection or backlighting that loose intensity and/or burn out eventually. The electron guns in the CRT loose intensity with age.
I have not heard of LED TVs wearing out but they are limited in size due to the inherent size for the diodes, image resolution and graininess. They are also pricey for the screen size.
To fix a fading or dead bulb you replace it. They are not cheap. Some sets you can do yourself, some require paying a tech $100 an hour or more. Check before buying on bulb price and if the consumer can do the work themselves.
Last extended thread we did here at OSNN generally recommended DLP type TV's for large screen. Do a search on "Plasma" to find it.
Also be aware that DLP is new and there is no "significant life data" yet. i.e. Nobody knows what will really go wrong with a million plus sets after 3, 5, 10 years. I know that I have a 20 year old CRT set, a 12 year old CRT and an 8 year old CRT all working just fine. My 5 year old CRT monitor seems to be starting to DIM a little.
Research whatever you decide to buy thoroughly, Web, FAQs, reviews, etc. And make sure that screen glare and image brightness are adequate for the room where you intend using the TV. My family room and living room have the "glare from hell". Store display areas have the lights turned out above and black or dark walls to make the sets look good. I will give Walmart an atta boy here. Their TV display area is just as brightly lit as the rest of the store. BB, Circuit City, Frye's all have blackout areas for TV display.
If you hadn't guessed I've been shopping for a new big screen TV for a few months now and am not impressed. (That includes CRT's. They don't seem to care much about antiglare coatings anymore.)