Recently when I start up my computer, the monitor stays black, and I have to restart the computer manually several times before the monitor will come to life. Any ideas on why this is happening and what I can do to fix it?
I sometimes have this problem too, you can try to put your Mac in sleep mode :
wait for the Mac to finish booting, press Control-Eject then type the S key, then wake the Mac up, the monitor should be working again...
I know it's not a solution nor an explanation, but it avoids rebooting the Mac...
make sure you go to ATI's web site and download the latest drivers I have a feeling your on something old and doing updates to the OS does not help anything. What card do you have exactly? The RV350 is a chip
Before you go replacing your graphics card, a less expensive item to check is the computer's internal battery. I once had a Power Mac 6100 that had the same problem you are experiencing. It took anywhere between 6-10 restarts before my monitor would come to life. When I installed a new internal battery, that fixed the problem. The screen lit up on the first start up.