I had issues getting my HDMI output to work as well. My issue was definitely different than yours but this is the best resource that I found:
What is happening is that the uEnv.txt file on your BBB, specifies a resolution which seems to be working as you see the splash screen. After that the BBB changes the resolution to the best that it can based on the EDID info that your monitor\TV is sending back.
The best place to start (after reading through the wiki page linked above) is to try SSH'ing into BBB and see what, if any EDID info is coming through:
- connect to BBB via SSH (process can be altered to do it over ethernet)
- get EDID info (ignore serial stuff)
I also had found a list of other things to try but cannot seem to locate it now. Here is what I recall:
- turn on monitor\TV first, boot BBB & if it doesn't work try restarting your BBB (sometimes it will pick up the EDID after that)
- ensure that the video output isn't sleeping --> hook up a mouse\keyboard & move the mouse\hit a key
There is also info on the BBB HDMI wiki page about how to force a resolution that you could try. I never had to goto that extent.