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You've already tried the good stuff, reassembling, checking all connections, resetting BIOS (taking the battery out).
The blue port on the back is your VGA port, your 'onboard grathics' which is the display adapter your motherboard comes with built-in. Try removing your video-card and connecting to that instead, hopefully you'll get video out.
If you get video out now it's time to go into BIOS, hit F12 or whatever during the initial boot process and have a look around for any settings related to the display adapters/video card.
Also check to see if your video-cards fans begin to spin when you turn on the computer, I know it's not putting out any video but if the fans are/aren't spinning that lets you know it's got power and trying at least.
If you do all this and still can't get that video-card to put out video, or worse-yet the fans don't spin at all, the g-card might be fucked. It happens.
Last step is isolation test, exclude the possibility that the card itself is damaged by testing it quickly in a different computer (your housemates?) to make sure it's fine.
