"Unfortunately, it doesn't provide any help for a MacBook Pro, other than indicating to call Apple Support" (sic).
Au contraire. TS1574's title and affected products are thusly:
"Troubleshooting issues with no audio from built-in speakers on Macs
Products Affected Mac mini, MacBook, MacBook Pro, iMac"
As a result, the instructions of the article are relevant. To be sure, follow those steps, the last of which is to contact Apple.
So, by way of reminder, here are the steps to troubleshoot the audio on your MacBook Pro. There is no red light, so the port is likely fine. Headphones work, so clearly your sound card is fine.
1. Ensure an incorrect version of OS X is not installed. If one is, then reinstall or erase/install after backing up your data.
2. Remove any external audio devices from USB, firewire, etc.
3. Open Sys Prefs > Sound > Output
If Internal Speakers is listed, select it and test again.
If Digital Out is listed, confirm again that all external audio devices and cables have been removed.
If mute is selected, unselect it.
If the volume slider is low, raise the volume.
If the above simply doesn't fix it, the issue may be a corrupted plist. Apple Support might be able to help troubleshoot the issue further, per the last step of TS1574.
I hope it gets resolved for you. Good luck.