Is this monitor mounted horizontally (typical TV orientation) or vertically (ala Pac-Man)?
As for your technical explanation of the regulator's operation:
The voltage regulator is basically a linear (class A) amplifier with the input set to a fixed voltage and an output stage capable of handling a fair bit of current. As the input voltage changes and the load current changes, the regulator develops a voltage across its internal (or sometimes external) pass elements (usually a bipolar transistor or sometimes a MOSFET) needed to hold the output at the fixed, set voltage. An internal (or sometimes external) feedback loop makes it do this.
Since the feedback loop is so simple, failures are generally related to the thing being "completely broken" i.e. shorted or open. A shorted regulator will simply pass the input voltage directly to its output, so the output will be too high and will have all the input nasties present. An open regulator won't pass any power at all, and you'll have an apparently dead monitor.
Failures are usually due to heat, inordinately high current draw e.g. shorted component and a fuse didn't act quick enough, or unusually high input voltage.
Poor power quality can be due to a broken regulator or bad smoothing cap on the AC rectifier output. In the case of a regulator that supplies B+ (the main voltage on the board from which other stuff is derived), like the STR3130 on a WG k7000 series, bad power can cause all sorts of problems. In the case of a bad regulator or smoothing cap feeding B+, this tends to cause a horizontal blackish bar that scrolls up or down the screen or similar "wavy" effects since the power will be varying at 50/60Hz (depending on whether you're in Europe or the Americas), but other things can happen, too.
Most cap kits do not include the big smoothing cap that I just mentioned as it's, well, big, and it's also expensive and tends to not fail as frequently as other caps. It's also more tolerant of being slightly out of spec. You might try replacing it if you suspect power quality problems.
A picture of these white bars you're talking about might help pin down the cause.