When I hit control J to make the top part of the chest one object it scrambles the wooden boards into different positions.
I made sure that there was a target object just like you said but I'm still having this issue.
should I apply the mirror modifiers to everything on the top of the chest
Hey Pat.
If the parts you are joining ALL have the mirror modifier, then you don't need to apply it to any part. However, if some do and others don't, then yes you should apply it.
As for stuff jumping around. It's possible that the parenting might be causing that. So try unparenting but keeping the transforms so the parts stay in the same place. Then select all the parts with the one you want to join them all to last. And try it again.
I hope that made sense.
Let me know how you go!