If this happened to me, I would first suspect I hadn't completely connected the DC-in board cable. If I hadn't just replaced the battery, I would wonder if the battery was good. MagSafe power cable connect connections fail too, especially if they've been attached for a long time to a red hot DC-in board.
If those failed, I'd head to the genius bar!
My experience with the mid-2009 13" MacBook Pro 5,5 makes me suggest paying close attention to how the DC-in board's cabling is situated as you remove the motherboard from the computer, especially in relation to the microphone and the display data cable retainer. The replacement DC-in board I used had fabric wrapping around the individual cables to the motherboard. Consequently, there is more material to navigate between these parts on reassembly.
I managed to make it work, but if I had paid more attention to exactly how the cable was routed before removing the original, reassembly might have been easier.
On the mid-2009 13" MacBook Pro 5,5 the Airport/Bluetooth cable is different from the other three cables in this step. It's fabric wrapped, and its connection works in a fashion more like the display data cable connection, although it does not have a lock that releases by pulling a tab back over the cable. So, to those of you who are repairing this model, be careful. Prying upward is not the way to remove this cable. I played with it until I could detect which parts were moving which way and why. Although I can't say with precision how the connection works, I removed it by gently coaxing slightly up at an angle and back along the plane of the optical drive. The idea is to pull the cable back out of its socket while lifting slightly.
Too bad we can't post photos in the comments.
On my mid-2009 13" MacBook Pro 5,5 the display data cable was square with the motherboard, rather than at an angle. I'm not experienced with working on computer connections, but if I were going to describe this procedure, it would be more like:
"Grasp the plastic tab on the end of the display data cable connection, and pull it gently back over the cable, toward the DC-in board. The tab is connected to a flat rectangular 'ring' that locks the cable to its connection, and when you pull the tab, the rectangular lock will flip back over the cable, allowing the cable to be removed by pulling the same direction, parallel to the surface of the motherboard."
Here's where the mid-2009 13" MacBook Pro 5,5 makes its first major departure from this guide. No such connection exists. At least nowhere I could find on the motherboard.
Reid, I got my part on Amazon. I got the impression that the mid-2009 13" MacBook Pro 5,5 used the same part as the 13" 2011 model, but check it out. Here's the part I used: (661-5217, 661-5235, 922-9307) MagSafe DC Power Board - Apple MacBook Pro 13" A1278/ 15" A1286 (2009, 2010, 2011, 2012)
This is a terrific guide. My project, a mid-2009 13" MacBook Pro 5,5, was a little different, and the biggest challenges I experienced were places where my computer's connections were different than the model illustrated. So I'll share how that computer differed for those who might come up against the same challenges. I'll add those notes and illustrations in the sections that apply.
I lucked out with the two keyboard ribbon cables. I simply nudged them into place with two different spudgers—one to pry gently upward from underneath, the other to redirect that force to press the cable directly into its slot. I was anticipating a struggle, but it was a nothing.
Thanks for the great work, Andrew Bookholt, and everyone else!