Tom, you have unfortunately entered the terrible world of HDMI. 35' is a long run by HDMI standards. What brand of HDMI cable do you have? In this case, brand does matter!
You'll need to spend some time debugging this and here's the cleanest way to do it:
1) At 35' you need either an active cable or a Certified HDMI cable so you can be 100% sure it works. Your best options are: www.futurereadysolutions.com and getting a KORDZ cable, which is THX-certified for 4k/UHD 18gbps. You can pretty much be 100% sure when using this cable. 2) Go with a BlueJeansCable.com cable. Again, BlueJeans is excellent. 3) Get a RedMere cable from www.monoprice.com. RedMere is an active technology that is made for passing the signals over longer distances. Don't believe any other crap about HDMI cables and plating, etc. It's all marketing garbage and hype. If I were you I'd go with the Kordz cable. A bit more $$$ but you can be sure it's been put through more high bandwidth, real-world tests by an independent tester (THX) and passed those tests than any other cable.
2) To test your setup, connect your equipment using a 6' cable. A 6' cable is ideal in the HDMI world. If the signal passes at 6' you can then assume that the longer cable is your problem.
3) To your question about AppleTV to projector works but not directly from Cable Box may be a bazillion reasons. You cannot apply analog logic debugging to HDMI. It's a completely different beast and will drive you nuts.
4) You may also have a problem with the compatibility of your cable box and your projector. For HDMI to work, they need to 'handshake'. That handshake takes a few seconds and several items need to pass during that handshake process including any HDCP copy protection and EDID information (what the display is, what resolution it can support, etc). All this happens in the background from source to display. If anything is not passed properly you'll get nothing, a blank screen, just as you are seeing. When you have a cable failing—and that may simply mean it can't handle the bandwidth supplied in the signal or distance issues, you get sparklies—that look like fireworks or snow across your screen.
The reason why putting the receiver in the middle causes everything to fail indicates to me that you may also have a loss of EDID information in the signal chain. A Kordz cable may fix that. If it doesn't then you need to invest in an EDID-based solution like Dr. HDMI. Check out these articles for more info: http://www.pooraudiophile.com/2013/12/the-fix-for-hdmi-woes.html and http://www.pooraudiophile.com/2013/12/the-fix-for-appletv-hdmi-woes-and-hdmi.html The second link specifically talks about the AppleTV
All in all, you have a bit of a tough debugging road ahead that will just take time.
You'll need to spend some time debugging this and here's the cleanest way to do it:
1) At 35' you need either an active cable or a Certified HDMI cable so you can be 100% sure it works. Your best options are: www.futurereadysolutions.com and getting a KORDZ cable, which is THX-certified for 4k/UHD 18gbps. You can pretty much be 100% sure when using this cable. 2) Go with a BlueJeansCable.com cable. Again, BlueJeans is excellent. 3) Get a RedMere cable from www.monoprice.com. RedMere is an active technology that is made for passing the signals over longer distances. Don't believe any other crap about HDMI cables and plating, etc. It's all marketing garbage and hype. If I were you I'd go with the Kordz cable. A bit more $$$ but you can be sure it's been put through more high bandwidth, real-world tests by an independent tester (THX) and passed those tests than any other cable.
2) To test your setup, connect your equipment using a 6' cable. A 6' cable is ideal in the HDMI world. If the signal passes at 6' you can then assume that the longer cable is your problem.
3) To your question about AppleTV to projector works but not directly from Cable Box may be a bazillion reasons. You cannot apply analog logic debugging to HDMI. It's a completely different beast and will drive you nuts.
4) You may also have a problem with the compatibility of your cable box and your projector. For HDMI to work, they need to 'handshake'. That handshake takes a few seconds and several items need to pass during that handshake process including any HDCP copy protection and EDID information (what the display is, what resolution it can support, etc). All this happens in the background from source to display. If anything is not passed properly you'll get nothing, a blank screen, just as you are seeing. When you have a cable failing—and that may simply mean it can't handle the bandwidth supplied in the signal or distance issues, you get sparklies—that look like fireworks or snow across your screen.
The reason why putting the receiver in the middle causes everything to fail indicates to me that you may also have a loss of EDID information in the signal chain. A Kordz cable may fix that. If it doesn't then you need to invest in an EDID-based solution like Dr. HDMI. Check out these articles for more info: http://www.pooraudiophile.com/2013/12/the-fix-for-hdmi-woes.html and http://www.pooraudiophile.com/2013/12/the-fix-for-appletv-hdmi-woes-and-hdmi.html The second link specifically talks about the AppleTV
All in all, you have a bit of a tough debugging road ahead that will just take time.