I have Direct TV (without a DVR) and older model TV with a cable input jack on the back and AV inputs on the front. The Direct TV box is connected to the AV inputs on the front of the TV.
I want to connect my DVD player and my VCR so I can view movies and possibly tape shows.

I've tried to connect them on my own to no avail. They use to be connected and worked with TV when I had Comcast instead of Direct TV.

You are connected to the TV using the Audio-Visual jacks. (usually Red, White and Yellow RCA plugs/jacks). You can connect the VCR to the Antenna or Cable input of the TV (RF input). When you use the VCR, you'll have to select that input and switch the TV to channel 3 or 4 (depending on how the VCR is set up).

The DVD player probably has Audio-Visual outputs also (Red, White, Yellow). Look on the back of the TV and see if you have another set of Red, White, and Yellow jacks. If you do, connect the DVD player to the TV using those plugs/jacks. To use the DVD player, you'll have to select the proper "line in" setting (Most older TVs have Line in 1 and Line in 2). Since you have a set of jacks in the front, it's likely you have another set in the back.

If this doesn't work, or if you still have trouble, please post back and explain what connections are on the back of your TV, the DVD player, and the VCR, and the DirectTV receiver.

Why did you chose to connect to AV connections not merely by cable to the rear.