I have an Apple MacBook Air A1370 with the same symptoms. Another descriptions with the same symptom/issue is "X on battery icon".

I've spent a month on this little Christmas Vacation Project, to get it to work for my son who is in elementary school and needs of a computer for class activity where the chrome book comes up short.

I bought it knowing that it would "not charge" and would "not power on". But I did my research online and on Apple's support/community website to understand how extensive the issue WOULD be to determined if I should gamble and make this purchase with an inexpensive fix.

However, after a month of research, purchasing of a battery and two trips to the Apple Genius Bar (they are no geniuses BTW), I think I gambled and LOST!!!

Here is what I know so far that may be of value to you....:

A new battery fixed the problem temporarily

A new battery from Amazon for ($70 incl tools) had enough juice to allow me to power up the MBA A1370 without the AC charger. I was able to see that it was a working computer. Shortly after seeing that the new battery allowed the MBA to power up without the AC charger, I put it on a charger, but did not pay close attention to the charging (or lack thereof) of the MBA or that there was an "X on battery icon".

My next focus was to resolve a "flashing question mark on folder when it powered up". So I went to the Apple Genius Bat (trip 1) for help with loading firmware and software.

Diagnostic helps

While at the Apple Genius Bar getting new firmware and software loaded (no CD Drive and Install CD to do this at home), they ran a 'diagnostic test' via there net software and the battery was not detected. It failed. There was a read box over the battery during their diagnostic test (on the display of my MBA). The Genius Rep and I both brushed it off as my replacement battery from Amazon was not OEM, so perhaps the battery was being flagged as a non-OEM battery. He went ahead and loaded 10.6.8 on the MBA (while on AC charger) which resolved my "flashing question mark on folder" after power up problem.

When I got home and opened the MBA it didn't "wake up", which I thought was odd because it was working on and off the AC charger while at the Apple Store. So I placed the charger on it and completed the set up of the MBA. That's when I noticed the "X on Battery Icon" and the information listed in "About This Mac" showed that there was no battery "installed" and "not charging".

Resetting SMC and PRAM

I researched how to remove the X on battery icon and saw that it could be resolved with resetting some things on the MBA.

Here are the steps for resetting the System Management Controller (SMC) that controls the way the MBA charges and acts under other situations. It did not work for me.

SMC RESET

1. Shut down the computer.
2. Plug in the MagSafe power adapter to a power source, connecting it to the Mac if its not already connected.
3. On the built-in keyboard, press the (left side) Shift-Control-Option keys and the power button at the same time.
4. Release all the keys and the power button at the same time.
5. Press the power button to turn on the computer.

I've read other links where these steps (or a version of) DID work for some people. See links below:

http://www.creativeblob.com/blog/macbook...

http://blog.laptopbatterylife.com/2011/0...

So I went back to Apple Genius Bar about the X on Battery Icon and they told me that my battery was "probably the issue" and wanted to sell me a new battery. I told them that this is problem exists on both of the batteries that I own (new and OEM), so it has to be something else. But the "Genius" said that they can only do the SMC and PRAM resets and replace the battery with an Apple OEM battery, to know the next steps. And doing a reset in the store did not fix the problem.

NEXT STEPS

So, we ordered the Apple OEM battery ($129) and I will be going back to Apple Genius bar for a third time to have them install it to see if this allows the MBA to recognize the battery and charge it ultimately removing the X on Battery Icon problem.

If the replacement battery does not fix the problem, it will be a $280 fix to replace the logic board (via Apple) and my bargain purchase is not so much a bargain purchase any longer.

....Worst case scenario...

As long as you keep the MBA on an AC charger, it works. But it is not advised to do this since that is not how it was designed to work and you'll be screwed if you lose AC power for even a second.

STAY TUNED..... In about four days, we'll have the verdict back on whether the Apple OEM battery fixed everything. If so, I'll be returning my battery I bought from Amazon.