Tinny audio and no boot chime

The early MacBooks never had that great a speaker system. Your system has two speakers just under the keyboard and a third in the back. Try using the balance control to bias the left and then the right to see if you can tell which speaker is having a hard time If you don't notice a difference you'll need to try a bass & treble recording to see if the rear is blown.

Often liquid spillage into the keyboard would damage the speakers. Sadly you would need to replace the upper case if either the left or right are blown Top Case with Keyboard Apple P/N: 661-5396 Follow this IFIXIT guide: MacBook Unibody Model A1342 Logic Board Replacement which will get you mostly there.

Here is the IFIXIT guide to replace the rear speaker which is a lot easier: MacBook Unibody Model A1342 Rear Speaker Replacement

While it is able to run the latest version of MacOS Sierra, Apple has made it clear this will be the last OS for it. So do consider the costs to fix the speakers as well as anything else it might need before going to deep here.

Here's the best image of the speakers: