Hmm, tell me, eddiebun, when you said you found a "two prong to three prong converter plug", I take it you're not referring to a common or garden UK shaver adaptor plug?
If you did use one of these, they usually fused with self-contained one amp fuse on the pin side of the adaptor body. A one amp fuse will only allow up to 230-240 watts to be drawn from the mains before the fuse blows. The LCD TV's power consumption might be greater than this figure, so the fuse would blow as soon as you switched it on. Even if it's rated at less than 240 watts, the initial power drawn by the TV for a few seconds after switch on, may well exceed this figure, again leading to the fuse blowing.
Find out the power consumption of the TV first before you connect it to the mains and never do it via a shaver adapter. You'll probably need to cut off the two pin plug and wire the two core flex into a UK standard three pin plug, obviously with no earth connection. A 3amp or 5amp fuse should be fitted in the plug but never a 13amp fuse.