I'm pretty sure that you're on a non starter there. Options of course are to keep your pc Outlook mail in a seperate folder after you've read it so that you can access that folder via the network. I'm assuming you don't use Outlook on the laptop. Could you not load Outlook on the laptop and then export the pc Outlook inbox to a pst file in my docs say, and then import said file with the Outlook on the laptop.
Better idea still , put Outlook on laptop, tell PC Outlook to leave messages on server after you've read them and then you would still be able to download the same messages to your laptop at a later date.
Is your Outlook on the PC web based or pop? If it's pop you could tell PC to leave messages on server and then access the same account via the web? most pops have the facility to leave messages on the server but as far as I've come across, web based mails stay read after they've been read.
Hope some or any of this helps!