Ran across this today. Ge dishwasher normal light just blinks and beeps when latch is locked. I had to replace the control module and it repaired issues right away. Hope this helps
Check the float that tells it whether to turn the water on or off on a fill cycle. Check the switch also. Its usually on a corner of the machine. - Great diagnostics!
There is a spring (or two, one on each side) that help return the door to the closed position (up) - I suspect that one or both of these springs have worn out/broken as this looks like an older appliance. If this is a built -in model, you should be able to slid the dishwasher out and look on the sides to see the springs.