On my Thinkpad T410s, I can hear the sound while using the headphones, but when I unplug the headphones it has no sound.
I turn up the volume button to no effect.
Typically the way a headphone jack turns off the internal speakers is by means of a mechanical shunt. The jack pushes a small piece of metal over - that disconnects the internal speakers.
When the headphone jack is removed, that shunt should return to the original position, that completes the internal speaker circuit.
If audio works through headphones, then likely the drivers and audio components are working correctly and either there is a problem with the headphone jack mechanical assembly, or a problem with the wiring for the internal speaders, or other defect with the internal speakers.
Try plugging / unplugging the headphone jack several times to see if the stuck condition can be resolved
Contact Lenovo service if the system is still in warranty if you were not able to resolve.
If your system is outside of warranty, and you wish to troubleshoot further, remove battery and power and dissassemble the system to allow access to the speakers. Refer to Lenovo Hardware Maintenance Manuals on the support.lenovo.com website for details.
Typically, the keyboard, palmrest and keyboard bezel must be removed.
Locate the speakers (typically 2) found on the left and right sides of the system and trace the wiring back from each speaker to a single, 4 pin connector located on the system board. Plug and unplug this connection to ensure there is no oxidation of the connectors which could inhibit the signal.
Trace the wiring and inspect it closely using a magnifying glass. Look for pinched spots in the insulation - these will appear as areas where the insulation has been flattened. Examine these areas carefully for cuts in the insulation that may expose the conductor in the wire. Sometimes, a wire may be pinched and over time, vibration from carying the system around can rub through the insulation causing a short.
The speakers and wiring assembly are typically low cost parts and would be the first thing to replace, especially if sound is only heard from one side, or only through the headphones.