How do I figure out whether my display is broken?

I initially had a problem with the GPU. I have since replaced the GPU and had a working iMac again! For like 3 days, then the screen froze on me again. I've tried rebooting, and I still get the chime. If I wait long enough, and try playing with the volume controls on my USB keyboard, I can hear the volume change click. I do NOT, unfortunately have an external Monitor that I can try.

I have actually ordered and tried a replacement LVDS cable, but It still has not resolved the Issue. I'm concerned that in my troubleshooting of the GPU, I may have damaged the connector on the logic board, or something else. My next step is to try replacing the LCD, but I was hoping to see if anybody had any insight on my issue.

Thanks!