@Applepie, did your Express come with a USB power adapter? They always did in the past, but it appears now they may not. If it didn't, make sure the one you're using can supply at least 1 Amp. Look at the fine print on the adapter and it should have something like "Output: 5V 1A". Anything greater than 1A is even better. Given that you've tried a few that may not be the problem.
You can try a factory reset, but it generally just gets you back to where you are now. With the power connected, use a paperclip or something similar to press and hold the reset button for no less than 30 seconds while ignoring anything happening onscreen.
The only other thing to try is another HDMI cable since a bad one can cause strange issues. If it still doesn't work I'd say it's time to return it.
The flashing light is often an indication that it's not connected to a network, but I didn't think it flashed like that until after it's made it through the initial setup.
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