How you figure out what's throwing up the message is art, not science, at least from the perspective of trying to do troubleshooting via Internet forum. It's one of those "I'd probably know it if I saw it" sort of deals. :) The precise wording would be helpful.
A few more questions:
1) Does TW use Motorola boxes or Scientific Atlanta or something else?
2) Does this happen with one specific channel or any channel? That is, when you get the "locked" message, can you turn to a different channel and it show up?
3) Is this happening on a HD channel? HD requires a better signal/noise ratio than standard digital, but even the latter can be severely impacted by signal problems.
4) When you are getting your channels properly, do you ever have any problems with screen lock (picture stops moving), black screen, or tiling (little squares showing up on the image)?
5) Do you have any Internet problems that you notice that are significant? (Longish periods of being unable to load web sites, slow downloads of large files, poor streaming of videos from anywhere other than YouTube (YouTube has its own problems and is not good for a test of this), etc.)
BTW, don't put too much stock in my "knowing." It's been awhile now since I did this for a living, and the technology has changed. But, I try to help where I can.
Anyway, given the timing of the start of this and the fact you have a digital box, I'm more inclined toward this being a "you are not authorized to view this channel" message coming from the box. I'm inclined toward that anyway. It is the "lock" wording that throws me because messages from v-chips tend to have that. This is also suggested by the fact it is intermittent.
This can happen in a number of situations.
If this is a signal problem, you're probably going to need to call customer service eventually regardless.
But, before that, there are a couple things you can do.
First, you can try not turning off the cable box for a few days (or until the problem happens again) and seeing if the problem continues. I say this because what could be happening is that your box losing its information about what channels you are authorized to watch when it is off and is having to wait on a refresh hit sent by the cable company. This can take a few minutes or a very long time if the cable company is weird or your signal is degraded. Note that this should not be happening. When you turn off the box, does it still have a clock or some display showing that indicates it still has power? I've seen people set this up so that when the box is turned off, they're actually cutting power to it, which will force a reset, and that will always take time for a refresh.
Note that even if this works, you'll eventually need to call customer service because it indicates a larger problem, perhaps a bad box or, again, signal problems.
Somewhat related to this, some companies send a system-wide RESET hit at odd intervals or after a poll of stored purchasing data for receiver side PPV programs, usually in the wee hours of the morning. This will cause the box literally to reset, lose all its programming data, then wait on a refresh hit. (There's actually a reason this is done, but it'd take too long to explain.) This should take no more than a few minutes and be invisible to you unless you happen to be watching the television at that time, but something could be happening that is preventing the box from regaining its programming information, which would again suggest a signal problem.
The powering-down the modem is really doing nothing but allowing time to pass. This is the reason it "didn't work" that time. It never actually works. It's just that enough time has passed for the refresh ... if this is indeed the problem. Tell him to stop messing with the modem. You can seriously screw up your phone service that way to the point you may not have service for days. Your signal is split at the splitter, with part of the signal going to the cable box, the other to the modem. These signals do not interact unless the tech has changed so much that they've completely redesigned the way this is done.
Also, check/replace the splitter. These can go bad, or they may have installed a poor one. (Some companies do this to cut costs.) You need a 1000MHz splitter. (What's on there now?) It'll say on the label. Don't get this at Wal-Mart, and if you go to a Radio Shack type of place, do not let them talk you into the Monster brand crap or anything that's gold plated. This stuff is pointless.
Something like this is good:
Geezus ... I start out to write brief messages, and I end up with these things ... I'm rambling. I took an sleeping pill and am fading and not being organized with my thoughts. You can rummage over that and see if any of it makes sense. I'll check in tomorrow to see if I can decipher what I said here and see if more can be done before the dreaded call to customer service has to be made.