Over Ethernet – no; you still have to find out its IP address and some kind of credentials.
The IP address might be easy to find using Wireshark or tcpdump (assuming it still has one by the time you've connected it; you might see it trying to get a DHCP lease from your laptop instead), but network access credentials cannot really be found or bypassed if all you've got is the same network access – that's kinda the whole point of SSH or RDP requiring credentials.
So assuming you can't get that information from the server's (previous?) owner, you'll need to 1) shut it down, 2) decide whether you want to reset the credentials and get it back running, or whether you want to focus on getting data out of it. If you only need files – either boot a liveCD with a different OS, or physically take out the disk drives and connect them to a different OS. (A regular Linux live USB stick should do the job.)