This can be done with the current capabilities of Rockbox. You would have to modify the settings file (.rockbox/config.cfg) on your computer for the proper settings, such as volume and repeat mode.
You would also set the start screen to Resume Playback. This will switch to the "While Playing Screen" on power-up and resume playback.
You can read more about these and other features in our fine manual (see the link on the left of the page).
Edit: This will only work if you have something to resume. If not, you would need to copy a couple of files from a working unit so that it can resume.