It sounds like the 480p/1080i input will not support the 990's menus or any video that the 990 transcodes from the composite and s-video input because those sources are all 480i, but the 480i/480p input will not support the HD signal from your HD cable box. If the 480p/1080i would also support 480i (doubtful from the name, but it can't hurt to check), then you could connect the 990's monitor output to it and use that for all video switching.
If the PS2 and your DVD player both supported 480p output (your DVD player will if it is a progressive scan player, with nearly all new players are, but I haven't messed with the PS2 enough to know what output options it offers), you could connect all three devices' component outputs to the 990 and run the 990's monitor output to the 480p/1080i input on your TV. In that case, I would recommend running an s-video cable from the 990 to the TV for access to the menu when needed.