This looks like your network may already be broken. By default the 3Com kit WON'T have Spanning-Tree enabled, the Cisco kit WILL. If you connect the Cisco switch and it detects an STP loop it will begin to block on whatever ports it sees as the Layer-2 'Worst' link (based on the STP root, port priorities etc).
I would draw a nice picture of your current network topology (including VLANs) and then work out if you have any loops and then try and engineer the Cisco switches into this network. Either that or pay for someone to come and sort it out for you.
I happily use 3Com & Cisco switches (and routers) together and as long as you know the limitations between them its not difficult.
Andy