I have Dell PowerConnect 6248, 48 Port for Private LAN. It's being only used for non-public network usage such as Backup, iSCSI, etc.
When I access to this switch or device that's connected to this private LAN, I have to go through a server which has dual NICs, both Public & Private setup.
My laptop is on the Public gateway, so I connected to RDP to a server, then connected to a device which uses Private.
Is there any setting I can do to switch-end, so I can directly connect to this private switches?
Sorry, I am not network engineer, and I don't want to be bothered by asking them.
Not really. That swtich does support layer 3 routing but doesn't appear to have any other features that would really help you out. Realistically you need some type of VPN solution. With a VPN solution you'll be given access to the private network through a secured channel without RDP or other means. Personally I'm a bit partial to Cisco ASA's / Anyconnect which works really well once you figure out how to configure it... there a tons of other options but realistically you're going to need to engage your network guys to help you engineer a better solution. If RDP (tcp/3389) is open to the public and that's the recommended solution for accessing your internal network then I'd probably be looking for a new job with a company that has a clue about how to properly design and secure their network.