Battery charges, but no light on MagSafe, indicator says "(Calculating...)"

For kicks, go to Applications/Utilities/System Profiler. Select "Power" from the menu on the left and paste the information here.

And just to be sure you're doing the SMC reset correctly, re-read the instructions here:
http://support.apple.com/kb/HT3964

And, no, it gives you no feedback when it's done.

As for doing a re-install, that's drastic. It might be worth booting from your Snow Leopard DVD and running both Repair Disk and Repair Permissions from the Utilities menu of the menubar.

If you still have the original install discs that came with your computer, one of them should say "AHT" or "Apple Hardware Test."
http://support.apple.com/kb/HT1509

I have read conflicting information about whether the AHT covers the power supply, but, hey, one more arrow in the quiver.

You can also-- carefully --try cleaning the socket on your MacBook. Read step 7 here:
http://support.apple.com/kb/TS1713

I had the same problem about three months ago with, my less than one year old Alu MacBook 13".
No light on the power cord
I made a reservation at the local Apple store's Genius bar.
After a few minutes of testing the response was logic board failure.

Did you replace it?

Apple replaced for me, free of charge. The MacBook was, and still is, in warranty.
I bought the MacBook AppleCare Protection Plan a couple of weeks ago, just before the end of the first year, just in case 😉
So that the three year rental is completely coverd.

I'm sorry that you had a bad experience with Apple.
Since 2001, I bought 7 Macs, the last 2 of them for rent. And a few iPods.
The only issue I had with all these products, was with the aforementioned MacBook, and an iMac.

I have the same issue as yours. My macbook is 2008 late 13 inch Aluminum model. It seems that the logic board for this unibody model is poorly designed, which caused the logic board sudden failed in normal use after only one year. I am also just out of warranty and Apple replaced the in-board Magsafe adaptor for me for free, but no luck, it still doesn't work. So I think your case is just like mine.

Actually, if you browse the former posts here, you can find something new. The magsafe adaptor actually charges your battery, but very very slow, maybe 1% for half hour, and the battery can only be charged up to 90% and that's it! If you look at your Magsafe adaptor LED light in darkness, you can see it actually dims instead of no light at all. So what i learnt is that the logic board can't recognize the adaptor for some reasons (overheat to burn the circuit?), then you can only keep the adaptor plugged in to charge the battery very very slowly to make the battery keep connecting with the power chip on the logic board. In this way, you may have the chance to keep the macbook running like what I am doing right now. But be very careful, you should never never let your battery drain. If battery goes to 0%, your macbook will sleep forever unless you can charge your battery in other similar model or develop an external battery charger for yourself.

B.T.W., I believe it's a common problem for many unibody series, especially for late 2008 first unibody model. So I strongly suggest we should complain to apple and ask them for a resolution. The reason why they didn't care until now is that only a few case presented and almost all of the unibody users just used their machine for no more than 2 years. The problem might come out more and more during the 3-year period.

I have the same problem however weirdly if you turn the magsafe adapter the other way up everythig is fine, I wonder whether it has something to do with the actual physical connections or the wiring that allows the magsafe to work either way up.