You could get the laptop and PC to talk to each other but for that you need a dedicated cable (null modem cable, null printer cable or laplink cable) to connect two serial or two parallel ports. The cables that you've got for your printer and/or scanner won't accomplish this. Also getting the software for this going can be a challenge in itself.
Getting the cable will take as much time as getting the new modem I'm guessing so this won't solve your problem.
Hope you're back up and connected again soon!