I have the exact same issue with my Syntax Olevia TV set. Like others have said I chalk this up to an HDMI handshaking issue. It seems like some TVs are more compliant with HDMI handshakes then others are. I had this same Roku hooked up to an older Samsung 27" HDTV previoulsy and the Roku worked fine. When I moved the Olevia into the bedroom then I would get the purple screen everytime I changed the inputs on the TV. The only way I could get it to reset on my set was to reboot the Roku box. Box is rebooted handshake signal is passed again and the TV and the Roku happily talk to each other (at least until I turned off the TV or switched the input later). It was a bit of a pain. I can move this same Roku XD-S to any of my other TV sets and cycle the inputs, turn the TV off and the Roku works when I cycle back to the HDMI channel. Only when I have it hooked up to this Olevia do I get the purple screen.
I believe this to be a TV issue and not a Roku issue because there was a bit of a fuss a few years ago with other off brand TVs (Westinghouse, Olevia, not sure if Dynex was in there or not) and handshake issues on the PS3 when it first came out. Lots of people on gaming forums complaining that their new TV would not display their PS3 screen and they had to unplug the cable between the two to get it to work. Some sets would display nothing others would complain that HDCP was not enabled between the set and the PS3 and would downgrade the video signal. To my knowledge, HDCP has been added to everything that has an HDMI port to help the motion picture industry protect their content. Some sets when they were manufactured did not completely follow the HDMI specs (as some of those specs were still being fleshed out while the sets were being manufactured). Its frustrating that something that you bought doesn't work right because of standards that Hollywood mandate and other companies cannot follow. Simplified argument, but you get my drift.
Anyway what I did to fix my issue was use the Composite cable that came with my new Roku 2 box and plug that into the Component out on the XD-S. Hey the XD-S doesn't know that the end connectors aren't the right color right?
Anyway I had to cycle the connectors around a few times until the video and color worked out right, but I now have my XD-S working fine through Component on my Olevia and have not had a purple screen in a few weeks now. I can cycle the TV inputs anyway that I want and the box is always there and online. Now is this something you want to do? No idea. My XD-S and Olevia are both well out of warranty so figure if I blew anything up (Wouldn't be the first time) it'd be all on my head. Guarantee you this is something Roku would suggest against, but being that the box is mine figured why not try it. Off hand I do not remember what final combination worked for me (Not home this week to look either), but it wasn't that hard to figure out. You do get some awful funky colors when the cords are plugged into the wrong port though (Like my wife commented she always wondered how the Predator would see Netflix and we think we know now).
Hope this helps.