when you say "for a while" is this PRE El Crapitan as well? can tell you I have: Crapitan 10.11.5 Fusion 7.1.3 Windows 7 Pro SP1 IE, Chrome, Firefox all browse fine in the Guest OS ...
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when you say "for a while" is this PRE El Crapitan as well? can tell you I have: Crapitan 10.11.5 Fusion 7.1.3 Windows 7 Pro SP1 IE, Chrome, Firefox all browse fine in the Guest OS Network Adapter is set to BRIDGED (which I suspect is the key to your problem) ...try playing with the network adaptor settings in VM (NAT/Bridged and Host-Only) and fire your works techie if he cant fix it
