Which tuner card is inside your son's computer? I don't see anything that looks like a tuner in your signature (which I presume is your personal computer in any case)...
Older tuner cards essentially took analogue SD (NTSC signal). For this to work with digital telly, yes, you would have to pick up a digital converter box from the cable company. Depending on the box model it could output video through a variety of connexions, some of which the tuner card might accept (or perhaps even the monitor directly). I've noticed that the newer cable box at my parents' house has everything from HDMI to FireWire.
If you have a new 'HD' tuner card, it likely can also read ATSC and clear QAM. ATSC is 'over the air' broadcast digital TV -- ie you need an antenna. QAM is the signal used by cable companies, but only some of the channels may be available unencrypted ('clear QAM'). FCC mandates that any channel available over the air (eg the major networks) should also be available on cable unencrypted. Some cable companies also don't bother encrypting 'basic cable', and so those stations may be available as well. Encryption seems to have increased over time (a few years ago, my friends could even 'inadvertently' pick up HD premium channels).
The cable companies' encryption of QAM and the lack of CableCARD tuners outside locked computers renders making a fully-fledged HTPC (with DVR capabilities) extremely difficult.