At this point, it’s usually the CCFL tube when it’s not LED, sadly. Now yes, sometimes it’s a bad inverter/power supply or bad capacitors, but that’s not the case like it used to be with many of these. Unless you get lucky and fix it with capacitors or a cheap inverter/power supply, it’s usually not worth repairing these monitors. It comes down to how hard it is to find the raw tube (most were recycled years ago, or they’re tired) and bare panels (again, usually they get recycled now and if you buy a used one, it may not have much left to give). SOMETIMES you can still find the tubes, but it’s not easy today due to the bulk of them being recycled due to the mercury.
You can try the capacitors as it’s a known issue with these monitors being from that period, but if that doesn’t work it’s time to give up and get a new one. Check both the power supply and controller board. It’s usually the power supply, but you want to check both to be safe with these capacitor plague monitors.
Personally, I’m at a point I will not fix a “capacitor plague” CCFL monitor unless it’s special, because the odds of the tube being bad aren’t in your favor these days compared to what the odds were 10 years ago (8 years from when I did the AL2216W for iFixit). By special, I basically mean it’s a unicorn matte 16:10 IPS with 1920x1200+ panel. These unicorn displays are often runover from when LED wasn’t mainstream in the pro market due to the color temperature not being there at the time for the pro grade displays. When I say pro, think HP Z, Dell Ultrasharp (5:4/16:10 IPS with factory color calibration), high end SyncMasters (again, see the note about Dell), NEC and ASUS PROART. Don’t let my refusal to bother anymore stop you if you insist on trying but keep that reality in mind.
Now yes, when we talk about modern LED panels with things like IPS panels being a standard feature since the market finally decided to leave TN and 16:9 behind to die outside of retailers like Walmart, 2K/3K/4K/beyond 4K things are a lot different — while I may not fix a 16:9 monitor from the era of CCFL as those are all low-res, I will work with a 2560x1440 monitor as the issues with 16:9 is beginning to get resolved with high PPI panels. 16:10 is also coming back as well, especially with high end monitors like the LG UltraFine, PROART, NEC, high-end Dell Ultrasharp and HP Z displays.