Converting your system to digital is possible, but it would be involved. You can use the existing component cabling with a hdmi conversion system that utilizes the 1 or all 5 of the existing component cords to each location. You're looking at replacing the main control unit with a new matrix switch as well as a receiver in each room - on average that'll be about $600 for each room that gets a feed from the main system, and about $2000 for the matrix switch. There would also be added configuration and setup of everything, and possibly a new remote/control system to operate it all. Overall, expect to be in the $5000 range to update the complete system.
But, you'll find this isn't just an issue with dvds, and eventually you'll have no choice but to update. It is getting difficult to find any analog only devices anymore. No bluray player will output analog, and most new cable/satellite boxes won't either. For those that do, you're limited to standard def (not hd) and no content that is encrypted (no hbo, no espn, etc). Same will go for any "smart" functions like an appletv, netflix, etc.
If you'd like help finding a local dealer/installer that can upgrade your system, or would like more input on specific options, I'd be happy to advise further.
If you want to forget about the control 4 system and don't truly need distributed audio/video, you might want to consider just a standalone system in each room. It won't be quite as convenient or advanced, but the cost would be a fraction of a whole house system.