If you can't restore it via DFU mode, then you're pretty much out of luck.
Edit: I downloaded an app before going to sleep last night, however I used it and saw no change in my phone, I'm not sure if that helps or not.
This sounds suspicious... what app was it? Is your iPhone jailbroken?
It was a game from Big Fish Games called Puppetshow .. And no my iPhone isn't jailbroken. However I did find a solution.
I basically wiped the entire phone out using a second computer, in hopes of restoring it to a previous restore point on my own computer. But that was a fail because the only restore points I could find were from that same day, and they didn't help because it would still give me the same result of the flashing screen.
My answer to you would be to wipe out your phone on a second computer and then try to restore it to a previous point on your own computer, a restore point before you started having this same problem. I couldn't find one, so unfortunately when I did this all I had on my phone was my contacts and most of my apps. Total pain in the ***, but good luck to you anyhow.