|"....the date on the back of the monitor is 2002."|
I said your model first came out in about 2000, because I found a review of it on the web that was dated in 2000. Reviews tend to first appear shortly before a model is released in large numbers, or within months, or within a year, of when they were first released. If the model sold well, it may have been produced for as long as 3 years or more.
If there are local computer repair places, many of them have techs who have repaired CRT monitors in the past - some may even be certified to repair Samsung monitors. You could take the monitor there and have them analyze it, that should establish whether it's worth fixing, but most places no longer do free estimates on CRT monitors and you would probably have to pay a fee even just for them to do that, and your CRT tube is probably going to have the problem of at least one color being too weak in not all that long a time.
The very fine lines you see on a Sony Trinitron (or similar name) display are support wires that support the grid of pixels. Some other monitor makers used the same technology in their CRTs, licensed from Sony. The support wires were of no concern until Trinitron CRTs were used on computer monitors, because you're not likely to be as close to a TV as you are when you use a monitor. Most people are quite happy to ignore that because of the superiority of the Trinition (or similar name display, including longer average useful display life (on a CRT). The pixels are rectangular rather than round. When they first used the Trinitron technology way back on their TVs, in the 70's, there was no other display that was as good.
When anyone asks me whether they should continue to use a later CRT monitor, my answer is keep using it until it no longer produces a good enough display. The later CRT monitors have mature technology that have some features that are still better than any modern display.
Getting a new monitor just because it takes up less space and uses less power is NOT a good reason to stop using a later CRT monitor that works well.
If you get a new LCD monitor, I recommend that you don't buy the cheapest lesser known brands and models, or even cheap models of some well known brands. E.g. Acer make cheap models, but they don't even have specific monitor drivers for them. Having specific monitor drivers available that you can load sets Windows, by default, to use only the settings both the monitor and the specific video drivers support, for the monitor. When you use Plug and Play Monitor drivers in XP or 2000, or Generic PNP drivers in Vista or Windows 7, you can choose settings that can DAMAGE LCD (and Plasma) monitors or displays.
The backlight(s) that produce(s) the white light that is filtered through the liquid crystals is(are) often warrantied for only one year, the rest of the monitor often for longer, but from what I've seen, brands known for superior quailty tend to produce a good display for the longest time. They're CCFLs - Cold Cathode Florescent Lamps - the same as for other florescent bulbs, they produce less light as time goes by, and eventually burn out.
A friend of mine bought two Samsung 19" LCD models - about 5 and 6 years ago now - one a monitor, the other a combo TV / computer monitor - she used both as monitors 99% of the time - both still worked fine, until she died in June of this year. She was disabled and had them on most of that time, for at least 3 years, 24 / 7, using a screen saver - the last while I had the system set up to shut the monitor off after xx hours of activity, so they weren't on during the night and during periods in the day when she wasn't using the computer.
If you want a display that will probably produce a usable display longer than a regular LCD display and the average CRT display, there are alternatives if you willing to pay more money.
E.g. Plasma displays, and LED LCD displays which use leds for the white light source, in theory, should last a lot longer, however I haven't seen that available in computer monitor only model - I've only seen that in combo TV / computer monitors - LCD or Plasma or LED LCD TVs that have VGA or DVI or HDMI inputs. The smaller display sized models of Plasma TV / Monitors are probably the cheapest.
(They're listed and advertised as just Plasma TVs or LED LCD TVs, but most if not all also have computer monitor input jacks, sometimes HDMI input ports.)
LCD displays are not anywhere near as good as displaying motion on the screen as the later CRT displays are - it's blurred. The original LCD technology is 60Hz, later on they came out with 120Hz and 240Hz technology; the higher the Hz, the more you pay. However, you can still get a better than average display with a lower Hz technology if you buy a quality brand such as Samsung, Sony, or LG.
Motion on the display looks best with the Plasma displays - 600Hz technology.
Another thing that is inferior about modern displays in comparison to the later CRT displays is they all have a Native or Optimal Resolution that they look best set to - all other resolutions will not look as clear, the most noticeable thing being text/fonts on the Windows screen will not be as clearly defined - although the display will tend to still look acceptable on quality brand displays. The later CRT displays do not have that limitation, at least not to the extent that you would be bothered by.
When you do use a resolution other than the Native or Optimal resolution, which is also often it's max resolution, you often can make the type/fonts on the screen look better by using this....
Turn on Clear Type in Windows XP or Vista - makes type/fonts on LCD screens look clearer.
Since modern displays do have that Native or Optimal resolution limitation which is usually also it's max resolution, you need to pay attention to that. If you want to be able to use that resolution, keep in mind that the higher it is, the tinier things will be on the Windows screen - that may be a problem if the physical display screen size is smaller, especially if you're like a lot of people like me who are older and their eyes no longer easily focus on smaller images and text.
E.g. if the physical size of two monitors you're comparing is the same, it may be wise for you to choose one that has a lower Native or Optimal resolution.
Also, make sure the video adapter you have has specific video drivers that can support the resolution BEFORE you buy the monitor, otherwise you're going to need to upgrade the video adapter in order to get the best looking display.
(E.g. look at what resolutions you can set the monitor to in the Display Properties, when it's set to Plug and Play Monitor or Generic PNP Monitor. )