It is against the law, currently, to upscale DVD over component video for copy protected DVDs. It has NOTHING to do with component video cabling itself which has no issue carrying 720p, 1080i, and even 1080p video. But, for copy protection, you won't find a player on the market which does this upconversion. At least, not legally.
Some players may be hackable to allow this, but typically the answer is to use your HDMI or DVI input on your TV to accomplish this. Better yet, Blu-ray can output up to 1080i over component and looks a fair bit better than any upconverting DVD player.
Yet, if BD is beyond your price point, I would wonder what TV you have with no DVI/HDMI input on it. If your TV has one, but is 'occupied', then go to Monoprice.com and pick up an inexpensive HDMI switcher.