It was connected to a cable box with composite. It was widescreen, so she thought that was "HD". Just didn't know any different.
Right, which is kinda what I was getting at when I said that 90% of people don't know the difference. So figure out how much you want to spend, how big of a screen you'd like to have, then see what name-brand stuff is in that range and has good objective reviews.
I mean, it's 2011, and the guy is asking his 4x4 buddies what he should buy to replace his CRT.

You basically only have two types: Plasma and LCD. LCD has three sub-types: cold cathode fluorescent backlit, LED edge lit, and LED backlit (with localized dimming capability). The age of the tech and the cost basically goes in that order, too. Plasma is the oldest and cheapest, then LCD. Once you decide how big of a panel you want, you'll probably find (especially in the +50" range) that the plasmas are much more competitively priced than the LCDs are.
(Side note, your computer monitor is an LCD)
Plasmas have good picture quality, but they gradually wear out (over a ~10yr span). They also generate a lot of heat. Figure a plasma will consume 200-300w more energy than a comparable LCD. Of the best-rated panels for picture quality, they're nearly all plasmas (with a couple of Sony LCDs thrown in). Part of that is because of the way a plasma works -- the panel is made up of thousands of individual pixels that can be turned on and off individually. So you get great blacks (because those parts of the screen are just "off").
LCD is more energy efficient (figure 100-150W for a big panel vs 350-500W for Plasma), doesn't suffer from age degradation, and doesn't suffer from burn-in. The CCFL tubes will burn out over time (again, 5-10yr lifespan), but are replaceable.
If you're playing video games or watching sports or news, LCD is the way to go. Anything that stays up on the screen long-term (like ESPN's ticker) will burn in on a plasma and remain there as a ghost. It takes a while for this to happen (think days/weeks), and newer models are better about it, but it can happen. You can burn over the entire screen to erase the ghosting, but it decreases the lifespan of the plasma when you do that.
As far as LED goes, most of your cheap LEDs (anything under $2500) is edge-lit. That means the LEDs are around the outside of the screen and make the whole panel glow evenly. This is no different in function from a CCFL backlight. The only problem is that you don't get good, dark blacks. You might get better longevity... but I'm not convinced. With LED lights in buildings, we're still only seeing 7-10 year lifespans, and those numbers are often based on percentages of dead diodes. You might have to have 30-50% of the diodes burned out before the lamp is deemed "dead".
Hmm... this is getting long, so I'll make a quick mention about brands and features.
Lots of companies are offering some built-in internet connectivity in the TV. Basically, plug an ethernet connection into the TV, and it'll get on the internet and play Hulu or Netflix or something. The quality of these offerings varies WIDELY, and I'd highly suggest reading some reviews on any particular manufacturer's system before using that as a deciding factor.
Make sure the TV has at least 3 HDMI ports. More is better. Figure cable box, xbox/ps3, receiver, camcorder, your cell phone, etc... all use HDMI. If you have any old components you'd like to keep (DVD players, receivers, etc), make sure that the TV has enough inputs of the right type to accommodate those other things. You'll want to have component-in jacks (Y/Pb/Pr) for the DVD, composite for your N64, etc.
Stick to Sony, Samsung, Panasonic, LG, Vizio... maybe a few others. I'm partial to Sony, but I was raised that way.

Dad's worked in broadcast TV for about 35 years. They buy hundreds of panels a year, all different brands. But any screens "that matter" are Sonys.