Are both identities against one ISP account or are you mixing 'normal' mail with an ISP address with an online account?
Also have you set any mail rules (Tools/Message Rules) which are affecting incoming mail?
Have you checked 'View/Current View/Show All Messages' is selected?
I think it unlikely that BT cable problems would damage any software on your PC; it may interrupt transmission and corrupt messages though. The fact that one identity is functioning correctly and the other is not tends to indicate a setup problem of some sort.