I've got this ACER 24 LCD wide screen DVI running monitor connected to my XFX GTX 280 graphic card.
Every time I turn on my computer it says No Signal so I have to turn it off and back on to make it work. Sometimes it does turn itself on but thats just sometimes.
I had the same problem a while back when I upgraded my computer with a HSI 3870x2. Ended up the cards(Yes 2 of them) burnt up due to bodgy constuction(I have tons of cooling in my computer). Used to switch between to 2 monitor ports and magically bam it worked again until I turned off my computer.
Talk to the company/person you purchased it off because if it hasn't already died it will probably be about to go. OR you could try getting new drivers but I doubt this is the problem.