It will work fine. Your old box put out DVI/VGA output which was split up into separate connectors (it was not YPrPbHV but RGBHV.
The new box puts out YPbPr so you only need regular component cables (3 RCA). I believe that you can select this in the menu of the Mitsu TV. It's been a while since I saw one but it is in there. Check the owner manual or just look around.