Hi Mike,
On one of the 6941 ip phone, Press Settings >> Admin settings >> Network setup >> SW port setup / PC port setup
Let's make sure the PC port is configured as 100 full.
Please have in mind that the CP-6941 is integrated with a 10/100 Ethernet port, so a higher speed like 1 GB will not take effect.
Reference: http://www.cisco.com/en/US/partner/products/ps10344/index.html
Try connecting any other phone model on same switch port and check if it works fine.
HTH
Manish