lem.halili , Did you check all the radio fuses, #8 30A under hood fuse block, Drivers side interior fuse panel #2 7.5A, #11 20A , this fuse may also be tied in (room) fuse its a 15 amp fuse. You should actually get a DVOM or test light and check all the fuses. If all fuses look good you may have to remove radio (link #1 below) and test for power at the plug, if power is feeding radio then radio is defective and needs repair/replacement. I also posted a link #2 to a trouble shooting forum for similar radio issue and a link to your owners manual. Good luck.
I hope this helped you out, if so let me know by pressing the helpful button.
https://www.youtube.com/watch?v=sG77cRRaWPM
http://www.rx8club.com/series-i-trouble-shooting-95/finally-display-head-unit-problem-solutions-209383/
file:///C:/Users/Home/Downloads/2005-mazda-rx-8-30095.pdf