I think the issue here is that the OP does not have an HDTV.
Unless the digital DVD recorder has multiple digital tuners, you will not be able to go that route.
The cable company should be able to provide you with a DVR (at cost) that will allow you to watch one channel while recording another.
Purchasing a cable splitter and another converter box would also work, but unless your TV has multiple inputs, you'd also need a switch to make swapping between the two sources easier.
Unless you previously required a set top box from your cable company, you will not need a cablecard solution. If you have a PC near the TV, you could make some updates (add a dual-tuner TV Tuner card and analog output) to it and connect it to the TV. This is...