You should perhaps more specifically define "broken" in the context of the discussion.
As I said earlier, measuring the C on an open cable is way easier than TDR. I have all sorts of stuff for TDR (7S12 and such), but If I were to do fault-finding searches in my house cable plant, I'd start with simple continuity measurements, then capacitance. It's a PITA to set up for TDR, and interpret the results - especially for a novice.
You'd have to find the proper cable velocity factor and impedance, match the impedances, and do a bunch of figuring out and interpeting* what's going on. With a C-method, you just need simple quantity measurements and simple calculation of the measured C divided by the C per foot to estimate the distance from the test end to the break.
Here's an example site with some info - one of many easily found:
I'm guessing that the purpose is to estimate the location - like in a wall or such, to assess the grief associated with repair. Or, to figure out who will pay for the repair - the cable company or you. Generally, the cable company owns and maintains the outside plant, up to where the service enters your house. So, all you need to worry about is from that point inward. If you can confirm that your cable is intact from there to the modem, you're all set. The point of demarcation should be the safety ground connector, where the company's cable enters, and your cable leaves. There will be a fairly heavy ground lead attached, that then runs to a convenient earth ground like a metal water pipe or ground rod.
If the cable goes from there directly to the modem, it's just a simple continuity test. If there is indeed an open, then the C test can help see how far it is from either end. If the cable is part of a distribution system in the house (your inside plant), then there may be all sorts of splices, power splitters, possibly amplifiers, and other cable boxes and TVs, etc, that will interfere with simple tests and TDR* too, so you have to know what's in there and where everything is physically.
If you already have it isolated to a single run of cable, and just need an answer, then keep it simple. If you don't have it isolated in this way, then unknown devices or connections may confuse the issue regardless of methods. If, on the other hand, you want to learn about TDR, then this is a good place to do it, so carry on.
*Notes from above - imagine launching a TDR pulse into any port of a black-box house cable plant loaded with all kinds of devices, with all kinds of cable interconnect lengths, and what comes back. Virtually none of typical devices are broad-band matched, so there likely would be a very interesting, but useless picture. You'd still have to have more info about what's in there, and isolate it to a single run for best results. A frequency domain approach would be a better alternative for at least proofing the whole plant, as-is, RF-wise. For example, put a VHF test signal in at the head, and look for it coming out at reasonably proper levels at each port.
One last note - I would advise against anyone arbitrarily hooking up a TDR system to any cable plant, whether it's for cable or satellite service, without first being absolutely sure that no DC power is present, or can inadvertently be applied. DC is often used on the cables for powering and signalling remote and in-line devices, so could damage the TDR equipment - an expensive lesson indeed.
Ed