I have an Inspiron N5110 that I was given to fix.  When you boot the computer up cold the display doesn't turn on, No BIOS splash screen, just nothing.  The computer keeps booting to Windows as I can hear the startup sound when it has finished loading.  If I reboot the computer everything starts OK.  I can run it and have no issues.  As long as it has run for a while I can power it off for a short period of time, turn it back on and it starts up again OK.  Once it goes cold for a period of time and I restart the issue returns.  The BIOS was an older version so I did update that, but it didn't fix the issue.  There is a post with a similar problem to mine, but it was never resolved.

Thanks for helping.