video doesnt show on my tv. whats wrong with it"?

well i bought my old xbox 360 about a week ago (stupid idea) for 20 bucks. the guy said he just plugged it in the day before to see if it worked & it did. just his old renter forgot it when he moved. i brought it home & tried to plug it in. didnt show picture but the green light turns on. occasionally the red turns on but most of the time its green. i looked up what the problem is & people say i should buy a component cable since my tv is an hdmi tv & the xbox doesnt have an hdmi port. i tried the component cable & it still doesnt work. is my xbox broken or is it the tv? ( i know the comp cable works because it works with my ps2) please help :(