Is the screen broken or the system isnt reebooting? if its the screen you can have it replaced for cheap,
http://shop.ebay.com/?_from=R40&_trksid=p3907.m570.l1311&_nkw=iphone+4+screen+replacement&_sacat=See-All-Categories%3C/a

if its not powering up go to apple and tell them it just stopped working just like that.