There’s no speaker connector on the classic II, just like the Plus it’s integrated in the main LB connector.
Is sound working after boot up? You can check this with a system 6.0.8L (make sure there’s an L!) boot disk by navigating to the sounds control panel and adjusting the volume from there. I’m not sure system 7 lets you do that from an install floppy.
If you don’t get anything from the built-in speaker, try the headphone jack.
Also, you could ask the person who recapped it if sound was working on their end... could be an analog board issue...
For the hard drive, I suggest creating a system 7 disk tools disk and a lido 7.5.6 disk. Lido is great for formatting or diagnosing if there’s an issue with the scsi bus or not. It won’t test the whole thing but you should be able to see if the problem is logic board related or hard drive related.
You just need some drivers / tools - and for sure a suitable 25/25pin straight cable as scsi cable. If you have another Macintosh with OS 7.x available, I can send you my files/images it depends on your startup disk whre to put the iomega driver file. usually you have to put it under the System Folder .. take a look on my Video - sorry, it's long and only German audio .. but should help a little:
Traces around there do look good, but a lot of those vias where all the solder has been eaten away do not.
Grab the schematics and check all traces in the startup circuit. Even if they look good they might have failed in places you can’t see.
Those 74s logic chips could be bad as well but I would start with checking traces first.