First off, there's no technical reason you NEED HDMI. Component cable will handle the best signal any source you have.
That said, I agree with DMC's suggestion that you run component from the DVD/VCR to the TV and, to add to that, I'd also run component from the cable box to the TV as well.
Likewise, I'd run a coaxial/toslink cable from both sources to the receiver as well. This will take care of any digital audio you may have.
But, VCR's don't output a digital signal, only analog, and I don't know if all channels output a digital feed. Likewise, I'm not too sure that combo DVD/VCR player will output the VCR video on component*. You may need to run a composite video (yellow jack) cable to the TV if you want to utilize this.
In this case, I'd suggest you run a basic red/white analog interconnect from both sources to he corresponding analog inputs on the TV. This will provide an analog audio feed to the TV at all times. If you don't want to hear it, simply turn the volume all the way down.
Incidentally, this also offers you the option of not needing the receiver to be on when watching the nightly news or the kids are watching Sponge Bob.
Now, you most likely have an analog audio output on the back of the TV. I'd run this to an extra 2 channel analog (AUX) input on he receiver. This will feed whatever is on the TV (including the VCR audio) to the receiver for the times you want to utilize this. To do this you should check your TV's manual as to how to shut off the speakers and send the audio out those jacks.
* I've got a Toshiba DVD/VCR combo and it will send out both DVD and VHS video over composite but over component it only sends out the DVD video. Also, both send out audio over the red/white analog inputs but only the DVD audio goes out of the digital outs.