Yamaha RX-V3800 and component output question...

I think you'll need to spend a little money to resolve this. I would put in some sort of video processor to convert the VCR/DVD to an HDMI signal.

Probably the cheapest way of doing this is a Gefen GTV-COMPSVID-2-HDMIS. It will convert a normal Composite (single RCA) or S-Video signal to HDMI and it will also scale it up to 1080p or whatever resolution you want. It's a quick-and-dirty processor with some limited configurability. There's a brand new one on ebay for a $104 buy-it-now price.

If you want to use Component (3 RCA) from the VCR/DVD, then you’ll need to look for an older video processor, such as a Lumagen Radiance or DVDO VP/30/40/50.  These video processors will likely give you a better image than the Gefen unit above, but they are more expensive.

There’s a DVDO iScan VP30 (without power supply) on ebay for $265 buy-it-now.

There’s another VP30 on ebay with full accessories, remote, power supply and original box for $314 or best offer.

There’s a DVDO iScan VP50 (better) on ebay with starting bid of $200.

DO NOT GET THE DVDO Edge.  It has known power supply and stability problems.

 If you want a Radiance, you might find an older Radiance XD for something like $400-700.  Or a newer Radiance.  Just make sure it has component inputes (many of the newer ones only have HDMI).

You have mentioned 1024i, 1025i and 512p.  All these are non-standard resolutions that I have never heard of.  It could be that the older RX-3000 supported these and the newer 3800 is standardized on normal HDMI type resolutions (480i, 480p, 720p, 1080i, 1080p).  Or it could be that the RX-V3080 is not able to cross-convert the analog signals from your VCR to an HDMI resolution supported by the projector.

I have no idea if the image will be degraded.  When you use component video, there is absolutely no handshaking.  It is NOT a digital communications protocol.  Component video is old school analog video. 

Once analog video has been converted to digital video, the transmission of digital video over HDMI requires communication handshaking between devices connected using an HDMI cable.

The idea of "handshaking" is a two-way communication coordination.  This is only in specific digital protocols, such as HDMI or Ethernet.  Component video is completely analog and it's one direction only.  The DVD/VCR is just spraying out continuous analog waveforms with no expectation or understanding of what's happening on the receiving end.  When the projector received component video, it may go through an exercise of analyzing the waveforms to determine resolution and frequency, as well as to lock onto the screen refresh timings.  However, there is no communication or "handshaking" back to the DVD/VCR.

One thing that you could try is take your DVD/VCR and the component video cable currently attached to your TV and bring both closer to the project.  I assume the "TV component cable" is a shorter cable.  See if the projector will accept component video directly from this. 

Then go from there.   It could be the "long component cable" is not working well.  Or it could be that the V3800 is not re-sending component video in a way that works with the longer cable - or it is not compatible with the older 1080i component video format.