Something like that is not going to be a hardware problem, like a bad electronic component... no way, especially in the digital video world.
The 2 settings you mentioned are not necessarily the ONLY settings in the TV that might be blocking you from getting better black levels from the TV.
Sometimes the picture mode you are using will even cause odd effects like the brightness control not working right. So try different picture modes... even ones you think might not be useful (though Dynamic mode or other garish modes aren't worth bothering with). For example, you might be using a mode named Natural or Neutral, but that's not an accurate characterization and you can't get control over the black level until you select Movie or Cinema or Custom mode (not saying your TV has all those modes, but it may have some similar mode options).
You also want to be sure you aren't getting balled up in the 0-255 vs 16-235 thing in RGB mode, that will bomb your black levels bad... either making them perpetually too dark or perpetually too bright. You're better off with everything in YCbCr mode... in YCbCr mode, all video is 16-235 unless some product breaks the rules and makes 0-255 / 16-235 apply to YCbCr... not SUPPOSED to happen, but manufacturers do a lot of things that aren't supposed to happen.
Start with investigating the 0-255 / 16-235 issue... only problem is your TV may not use that nomenclature... it may have a menu option with Normal or Standard or Limited as one setting (those would all signify 16-235) or Expanded, Full Range, PC and those would indicate 0-255... but those aren't the only strange names manufacturers use to camouflage the real setting. And at least one manufacturer (Samsung) has managed to label the setting backwards for 5 years or so. Sometimes the setting is called Black Level, but as usual, different brands assign different names to it.
