I've never seen a laptop battery soldered in.
Usually they have a wire harness that leds to a connector on the board.
I'll give you some opinions and you can do what you will with them.
Buying mobos from eBay seems very risky to me.
I'd be more likely to buy that model like yours, selling for $100, assuming that it is listed as functional.
The new $150 board gives you a lot more assurance that it will work. Bear in mind that replacing laptop motherboards is tricky and if it doesn't work at first, you can have a higher level of confidence when it's a new board. Also, older boards get brittle and they are sensitive to being bent or twisted as you seek to manoeuver them into difficult spots.
Financially speaking, I find it difficult to spend $150 on a laptop mobo, unless it's a really high end machine that was worth over $1k when it was new.
If you spend $97 more, you can get a new laptop with a newer system with new capabilities with a new 4 hour battery, new keyboard and new hard drivve.
At $375 (minus the $150 for mobo), you can get a slick aluminum built Asus Ultrabook (I sell a lot of these) that has more power than your original machine, 4 hour battery, 4 gigs of ram, 500 gig hard drive, great webcam, very good sound, and one of the handsomest machines around.
It's worth taking the time to think about your next move.
Whatever you do is good, as only you know what's best for you.
Avoiding the worry about buying sensitive parts like mobos, new or used, then the installation time and the stress that comes with it not working properly the first time, or maybe not at all, has a certain intrinsic value, if you can avoid it.
Even I avoid those jobs as much as possible.
You never know for sure if the mobo is good, as there's no way of testing it and if it doesn't work at the end of the day, I know my clients are thinking that I did something wrong.
Lastly, you can buy one of these USB to SATA adapters for getting the data off your old hard drive, for $3.43.
All is well in Paradise.