Modules are assigned to content panes. If the module is assigned to a content pane that does not exist, it should be shown in the one named ContentPane.
So, if you change a pane name, the modules that were in the old pane should show up in ContentPane.
Do you have a pane named ContentPane in the skin? That is a requirement, so add one if you don't have one now. Then your modules should appear in ContentPane. You can test this by temporarily assigning a Gravity skin to the page. When you do this, do your modules appear?
You can also do this (somewhat dangerously) by getting into the database table named TabModules and editing the field named PaneName for those modules that are mis-assigned. Do something like:
update TabModules set PaneName='newpanename' where PaneName='oldpanename: