Will Apple TV work if I connected it to a DVD player? My TV does not have an HDMI input, so I was wondering if I could still use it by connecing the Apple TV to my DVD player's HDMI port instead?

My DVD player (Philips DVP3560/F7) is capable of 1080p.

Also, will Apple TV work with my (rather old) TV? My TV (Samsung TXN2668WHF) is capable of 1080i and 480p.
The apple TV 2 supports 480p. In my case it works through my AV/Amplifier which is connected with an HDMI cable to my TV.

The only catch would be HDCP which requires end to end protection of data. But from what I understand HDCP allows non HDCP compliant hardware to receive lower quality image using legacy connectors (RCA, S-Video ...). So it all depends on how your DVD player is connected to the TV.