Sounds like a power issue to me too, regardless of what lights are lit. How many HDD/SSD are you running? Optical drive? Bluetooth or WiFi? shut down or remove anything you don't need, and try again. Oh, if you are running WinDOHs you might have problems with that, though. Your copy might think you have moved it to a different computer. Check all your power connections. One by one, unplug and plug all the connectors then turn it back on. Could it be your BIOS? I don't think so, but I could be wrong. I think it is a power issue and it could be the PSU or it could be a high resistance connection. MoBo battery? Again it doesn't sound like it to me but if you can easily replace it then it would be good to do so just for shits and grins.
If you remove both graphics cards, does your mobo have onboard graphics? Can you plug in a monitor?
Once it is running again, I urge you to create a Live USB of Ubuntu. This could be useful in the future. Doesn't cost anything except the price of a USB thumb drive and a few minutes of your time. If your WinDOHs partition somehow becomes unbootable, the Live USB might be useful for troubleshooting and repair. Some darn good disk utilities there, too.
