Remove the absolute paths from your images. Instead, do this (assuming that everything is in the same folder, as per your question):
ul#header li a.logo {background: url("nav_01.jpg") no-repeat 0 0}
ul#header li a.home {background: url("nav_02.jpg") no-repeat 0 0}
ul#header li a.sugestology {background:url("nav_03.jpg") no-repeat 0 0}
ul#header li a.creator {background: url("nav_04.jpg") no-repeat 0 0}
ul#header li a.inbulgaria {background: url("nav_05.jpg") no-repeat 0 0}
ul#header li a.contacts {background: url("nav_06.jpg") no-repeat 0 0}
I would also advise putting the images in a separate folder instead - helps to tidy things up!
Update:
You are also using ul#header
in your CSS, but you do not have a UL with an id of "header". You only have "header" on the div, so you need to change your CSS to use a different ID on the UL. Alternatively, change your CSS as follows:
#header ul li a.logo {background: url("nav_01.jpg") no-repeat 0 0}
#header ul li a.home {background: url("nav_02.jpg") no-repeat 0 0}
#header ul li a.sugestology {background:url("nav_03.jpg") no-repeat 0 0}
#header ul li a.creator {background: url("nav_04.jpg") no-repeat 0 0}
#header ul li a.inbulgaria {background: url("nav_05.jpg") no-repeat 0 0}
#header ul li a.contacts {background: url("nav_06.jpg") no-repeat 0 0}