I'll agree with mfenn, partially. Again, it depends on your particular cable service. Cable systems MAY provide programs in four technical classes: analog or digital signals, and EACH may be either encrypted or unencrypted. Beyond that, the companies often package certain groups for marketing, so you can buy one group of "Basic" channels for a flat monthly fee, then add another group of encrypted ones for an add-on fee, then another group, etc. Anything unencrypted does NOT need a set-top decryption box. These MAY include older analog NTSC channels and newer digital channels not encrypted, called Clear QAM channels. The older ones you could handle with your old ASUS card. The newer ones would require a new card able to tune into Clear QAM channels. (By the way, the unencrypted new digital channels available as OTA signals broadcast locally to your antenna are called ATSC channels - their digital system is different from the Clear QAM system used on cable.)
As corkyg has pointed out, some cable operators will provide a set-top adapter for little or no money that allows you to tune in a digital Clear QAM channel from the cable and feed it to an older analog TV. Some set-top boxes used to decrypt the pay TV groups on cable may output an analog signal, but most are concentrated on digital HD quality stuff so you still need to feed it into a digital tuner system.
The "IR Blaster" accessory with many new tuner cards lets the computer's software send out IR signals (just like the remote that came with your set-top descrambler) to tune that box to the selected channel; then its output can be fed to your computer's tuner. A CableCard system (IF your cable operator supports this - check with them) allows you to install a special card in your special tuner card so that it takes over the descrambling task for premium pay-TV channels available on your cable, and the computer does not need to use the set-top descrambler.
IF you are considering a system that allows you to watch one channel while recording another at the same time (using the computer as a digital PVR machine), you will need a tuner card with two tuners included. Read carefully the details for these - there are a couple of different ways this is done, and some have each tuner limited to only certain signal types, while others have two all-purpose tuners built in.