I got my hinge and got a couple of hours. Repair done. For anyone trying to do this let me say that it is not for the faint of heart and not really something you should start and continue on a different day. Give yourself plenty of uninterrupted time to complete the repair. Take pictures along the way -- if for no other reason than when you blog it you can include pictures. (Whoops.) [Update: had to do it again - this time with pictures here]

If you've got the bucks and are going to keep the laptop for a while, consider maxing the RAM, replacing both hinges, upgrading the hard drive and replacing the power plug. Thankfully, Sony had the foresight to not board mount the power plug. Get the service manual too. For this model, there was only a compatible model's service manual (SM VGNA-130/B/P/170 Part#: 987636707). Call/email the parts place for yours.

1. First, leave it open at 90 degrees or so -- make sure you support the angle so you don't break the other hinge and possibly rip a display cable.
2. Power off.
3. Remove the battery.
4. Remove the keyboard by unscrewing the two dotted arrow marked screws.
5. Gently pry up the bottom edge of the left/right edge of the keyboard and lift up a little.
6. Locate the keyboard ribbon connector and gently work it out of the socket.
7. Under the keyboard there are two totally different screws that need to pulled out.
8. Now unscrew the fifteen million other screws from under the machine. I think you only need to remove the arrow marked screws. Most are the same size, but two are long -- use your screwdriver to scratch the case or use tape to indicate where they go. I don't think you need to remove the flush screws from underneath, but I think you might need to remove the two screws from the back edge.
9. Now the "palm rest" can be lifted with a little gentle wiggling.
10. Look for the two ribbons (mouse, speakers/buttons) that need to be taken off.
11. Remove the palm rest. Now you should be able to see the base parts (feet) of the two hinges.
12. Now for the display bezel. Use a dull point to lift off the rubber covers off the screws in the four corners of the bezel. Unscrew them.
13. Now you will have to use a little bit of force to pry the bezel off, but be careful not to slip and crack/scratch the display. (That's a $700 part!) Also watch out for the hinge area of the bezel.
14. Lift off the plastic hinge cover.
15. Be sure to support the display while you unscrew the screws holding the arm of the hinge.
16. Then unscrew the foot and you should be able to slip the hinge part out without totally disassembling the display frame.
17. Slip the new hinge arm in and screw it down, now angle the display so the hinge foot is against the base flat and screw it together.
18. Now make sure that the display cable (both sides have some cabling) slips in the hinge without interference.
19. If you are replacing both hinges, replace the broken one first and screw it in before unscrewing the other one.