Using just this???

You can do it, but you'll run into issues keeping the CPU/GPU cool if you don't have a fan running on the radiator. Especially if it's the model with the built in Radeon graphics. As for powering it, just get a power supply off of eBay. They're only 5 or 10 bucks brand new.
http://www.ebay.com/itm/351547128878You don't really wanna try running it with just 12 volts, while it will work, you could be underpowering it and may experience crashing or simply shutting down once the CPU/GPU usage goes up.
For hard drive, you can just use a USB stick and set it to boot from USB. You'll wanna keep the keyboard connected while setting it all up, but afterwards you can ditch the keyboard... better yet, replace it with something like a Logitech K400+ and don't worry about it.
http://www.newegg.com/Product/Product.aspx?Item=9SIAB274YM8877That's what I use on my son's cocktail cabinet. It allows me to do maintenance and what have you without having to open up the panel to access the jacks.
To secure the motherboard down, just use some Jamma Board PCB feet
https://paradisearcadeshop.com/fasteners/21-pcb-feet.htmlMy solution to address heat dissipation on that radiator would be to just use a modified slot cooling fan over it... Would actually probably cool better then the stock fan would if you do it right.
Here's one example, but I'm sure there are many other higher quality ones:
http://www.newegg.com/Product/Product.aspx?Item=N82E16835200019Try searching for this:
http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&DEPA=0&Order=BESTMATCH&Description=slot+fan&ignorear=0&N=-1&isNodeId=1All tallied, I'm guessing around $50 in parts will get you a good start.
EDIT: And there is 1 more thing, now that I'm thinking of it.. You'll need a way to power it on, so you will
MAYBE have 2 options here.
One, solder into the power switch and run a lead to the side of the cabinet that way,
http://www.ebay.com/itm/232049348491or second, and I'm not sure if the BIOS has this setting but I think it does... Just setup the BIOS to power on after power failure, then you'd only need to rig a simple switch on the power supply cord to power up. I've never personally tried this on a laptop, but in theory it should/could work.