Any cable can be 'shielded', but most Ethernet cable is UTP (unshielded twisted pair) because it has less crosstalk, higher frequency response, greater bandwith and is easier to use because of the lack of shielding and the propensity to do STP incorrectly. Like ScottMac said, STP should be avoided except by professionals.
As ScottMac, Peter and Ben# mentioned, fiber is the correct use between buildings or whenever going outside. So Remy, your situation is a big problem. Replacing $500 boards, 6 at a time per storm is not a reasonable solution. This is attrition and waste through inadequate management and planning.
Fiber should also be used WITHIN the same buildings between floors and between sections of the building having different electrical services, transformers, major ground services, etc.
Electrical systems in buildings can have voltages where they should not, including voltages on ground (yes, I've measured this before). This is often one of the causes of problems. When grounds throughout the building are not equivalent, then problems occur to equipment within the building. Supposedly, using isolated grounding is better, but if the isolated grounds differ between other common grounding then problems occur.
Electrical storms can cause individuals to transmit electrostatic potentials to PC's, but as you said, the most likely cause is the lightning strikes and MODEMS or other intenet connection via the CO or WAN connections. Voltages and potentials can travel anywhere where there is a path of little resistance. So if the CO or a line somewhere gets hit, it could possibly affect your connections.
Since I don't know enough about electical service, I believe having power conditioning equipment like induction tranformers (large ones) to condition electrical service from the electric company might work well in conjuction with largee UPS systems with generator backup and active switching for each building to provide conditioned and protected electricity to outlets in areas requiring protection (ie, not the bathrooms, halls, etc).
It is possible to test electrical power service in buildings.
What about professional lightning rod installations where needed to reduce lightning strikes near the buildings?