Are both displays blank, or only one? Is there any backlighting coming on? Any cracks visible? Was there any damage (dropping, etc.) that you remember around the time they went blank?
If you determine that your phone is actually turning on, do the other functions of the phone work? In other words, can you dial a number and hit "Send" and successfully make a call? Can you get sound out of the external speakers by pressing the little "speaker" key at the lower right of the inside keyboard?
If everything seems to work and the ONLY problem is the displays being blank, it is possible to replace the display module. If you have some electronics experience, and you are considering doing it yourself, see this thread
for a little more detail about my experience (I did it successfully.) But you'd want to know that the display is the *only* problem before committing to replacing it.
Otherwise, there's not a lot of repair you can do on these things yourself.