It could be amost anything and without more details I don't think you'll get much useful help.
How is the Xbox modded (chipped, TSOP, softmodded)?
What dash was it seen booting to, a hacked one or original MS?
What region (PAL/NTSC) is the Xbox and your TV?
What cable connection type are you using ie. Composite, S-Video. Component or SCART and what was the seller using? The same cable?
What is the front LED light colour? Does it blink?
My guess, from the fact it was working before and now you've got it home you're not getting any picture or sound, is that it is a connection issue of some type, possibly to do with the cable or your TV/settings.