Defective Monitor or Video Card?

For the past several weeks, the display on my comp has been really flaky. To be specific, it won't come on immediately when I turn on the comp. I have to do repeated restarts to finally get it and then it only comes on in Safe mode. If I then do another restart from Safe mode, I can get it back into Normal mode. Once I finally get it on (in either Safe or Normal modes), everything works fine except for one game (Total War Attila) which may be a totally separate issue.

When I say it won't come on, what I mean is I hear the start-up sound effects at the usual time interval but the monitor remains dark.

Due to my living situation, it will be a big deal to cart the comp out to a repair shop so I'd like to avoid that if it turns out the real issue is I need a new monitor. Any advice is appreciated. Technical info follows:

My monitor is a ten-yr-old AOC, model 919Swa1, Resolution 1280 x 1024 x 60,

My video card is a NVIDIA GeForce GTX 560 Ti, bits/pixel 32

My hard-drive is Intel(R) Core(TM) 2 Extreme CPU X9770 with an X64-based PC

My operating system is Windows 7 Home Premium with Service Pack 1