IPhone – Charging iPhone 4S from closed MacBook Air

Yes - the SMC reset should resolve any temporary issues with the hardware not sensing the charge adapter. It's even called out in this KB article by Apple as something SMC reset can potentially address:

http://support.apple.com/kb/ht3964

Once you ruled out SMC needing to be reset, you should get the Mac in to a repair shop or do what they would do to isolate the hardware failure:

• test your adapter with another computer
• test your computer with another adapter
• test your computer with another OS (last resort - SMC and the charging behavior you report can be tested with the OS powered off and only the firmware / SMC regulating the LED color and charge state based on the data it can collect which is faulty in your case)

Once they have isolated the failure (likely to your computer), they would open it and inspect for any corrosion or damage on the logic board and charging circuitry and the either swap and test the magsafe board or the battery or the logic board itself based on experience and the hardware service manual for your model.

The fact that your computer shuts down at 50% remaining charge and also that your MagSafe LED remains orange makes me think that either the replacement battery isn't an official Apple part, that it is defective/DOA, or that your logic boards SMC is corrupted and needs to be reset.

If the battery is indeed new and Apple original than proceed with an SMC reset:

http://support.apple.com/kb/ht3964

This will tell the SMC chip to reset all power states and reboot so that it forgets the battery and MagSafe adapter momentarily and then rediscovers them.

Hope that helps