I read this topic title and thought "Oh no! A problem with the Sega laptops!"
Is it bad that I'm relieved?
Any ways in regards to your issue, are you able to see the POST screen (for Dell that usually is the Dell logo that appears when you first power on the laptop)?
If you're seeing that, then press Esc while that logo appears, it should provide you with the key to enter into the BIOS setup (usually F2 or F12). In the BIOS setup, you can change some options around. There maybe something related to power in there that might fix your issue.
The next trouble shooting step if you still can't get it to work would be to attempt to start windows in safe mode. Assuming you are using Windows, it is accessed by hitting and holding F8 on startup. From there you will see the option for Safe Mode. See if Safe Mode gets you in all the way to a usable version of Windows, from there a restart should fix all of your startup issues (if your original problem is not serious). If getting it to Safe Mode didn't work, then you might be looking at Power issues, Hardware Issues, or Software corruption. In which case your best bet would be to find a friend handy with computers, offer to share a six-pack and let them have at it.
Good luck to you.