If your computer is not making any sounds, see the Acer Aspire 5253 Has Volume Control Problems problem page for possible causes and solutions.
Here are the schematics for the motherboard, found from this website.
Go to p.27-28 to find the audio circuits.
Have you checked that the headphone socket is OK and connected properly?
When headphones are plugged into the laptop an internal contact in the headphone socket signals the audio codec IC on the HP_Plug# lead (see p.28) to switch the audio away from the main speakers and connect it to the headphone socket. It may be that the headphone socket is faulty and that the audio output is being permanently directed to the socket but it just doesn’t get through it to the headphones. Worth checking first anyway, if only to eliminate the possibility.