Gigabit Ethernet Questions

I have a PC running W7 Ultimate with two Realtek Gigabit PCIe Ethernet Ports onboard my Gigabyte P55A-UD6. I only use one at the present time (on occasion it's been beneficial to have one spare to use to set up another device), but I have rather a lot of video files I want to copy to my Home Server (HP ProLiant Microserver N54L with onboard Broadcom/HP Gigabit Ethernet, running Windows Server 2012 Essentials).

When I copy them across quite often I am swamping the connection on my PC (presumably my server too), by which I mean I reach up to 99% Bytes Sent Throughput. I have looked at the settings for the onboard chip in the server and unfortunately it appears it does not support jumbo frames (I've read they can help when transferring large files as it causes less CPU Interrupts), so I've bought a separate dual Gigabit Ethernet PCIe x1 Card for my server. However my current setup has 8 wired devices, I have a Linksys EA6700 Router and a Linksys SE2800 8 port Ethernet Switch, the latter currently has 2 ports free.

I have another 5 port Switch I can use so I was contemplating connecting both Computer and Server up using two ports each, however does this mean I need two Ethernet cables between a switch and the router? E.g. If I connect my PC up with two ports to the router, do I then need two cables between the router and the switch serving the server? Or can one Cat 6 Ethernet cable handle 2Gbps worth of Data?

does this mean I need two Ethernet cables between a switch and the router

The switches I've used had only 1 Uplink port for connecting to the Router so that would be a limiting factor.

The only time I've see 2 NIC/Network Interface Cards/Adapters in use on one computer was for connecting to 2 separate networks, check about Bridging, might work in your case.
https://www.google.com/search?site=&....0.TRErLbD7nUE

I know my Desktop PC has a Teaming Capability to effectively create a single 2Gbps connection, I'm assuming that with the Chips being Realtek ones the software and drivers might also have the Teaming Option, I shall need to wait and see.

I thought a single cable might be a limiting factor, however the Linksys SE2800 has Auto-Sensing Ports and has no specific uplink port, nor does the 5 port Gigabit Ethernet Switch (not Linksys) so I would assume that two connections to the switch might be a viable option, again I'll need to see if this is the case or not.