How to make a button jump to slide and change state view on a separate slide

Which version are you using? This is very important. Since you talk about states, I suspect you are using Captivate 9? However I am hesitant, because you talk about 'two states'? Normally a clickable object, like a shape button that can be filled with an image has already 3 InBuilt states: Normal, Rollover and Down. You can add a custom state, which could be a gray version of the image in the state. Have a look at this blog post, where I created several shape buttons with 4 states:

1 action = 5 Toggle Buttons - Captivate blog

If this is the situation, you'll have to use a shared or advanced standard action, triggered by the Success event of the Complete button on the last slide of a module. That action will look like this:

   Change State of SB_ModuleOne to Gray          SB_ModuleOne is the shape button on the Home screen, Gray the custom state

  Jump to Sl_Home

If you choose a shared action, the bolded words will be parameters. For two modules like you mention, you can use two duplicate advanced actions, only the shape button has to change for the second module.