While the DVD player is capable of upconverting to 1080p and has an HDMI output, the TV doesn't have an HDMI input jack, which limited my options for connecting. Furthermore, the component input jacks on the TV (YPbBr) have coaxial connectors rather than RCA connectors. Alternately, I can connect the video using S-Video cable, although this is still an analog signal.
What the TV does have is a DVI-D (dual link 24+1 pin) port, although I'll need an HDMI to DVI-D adaptor to make it work. Luckily, you don't have to spend hundreds of dollars to buy Monster Cable, but if you know where to shop, you can get your needs taken care of for under $10.