Your S2110 uses an Atheros SuperAG Mini PCI wireless card, it's located underneath its keyboard. Assuming this card has worked before, then it'd probably failed. I'd remove it and reseat it first. But you first have to dig the keyboard out and it's a little tricky but someone else had posted the S2110's keyboard replacement procedure on-line and here's the link (you're not replacing the KB but you can follow these steps to get it out of the way):
http://www.insidemylaptop.com/replace-keyboard-fujitsu-lifebook-s2110-laptop/
If you've reseated the Atheros card and it's still doing the same deal, then it's likely bad and you can replace it. You can get the exact model of the Atheros card and see if you can find the exact same one on eBay (that'd be your best bet); or you can get some other card (such as a Dell-branded Intel 2200bg Mini-PCI Wireless Card, drivers can be downloaded directly from Intel's support site) if you have trouble finding an exact Atheros replacement. The cost of such a card should be $10 or less.
Of course, there are other alternatives, too, such as a USB wireless device or a PCMCIA wireless card, which are just plug and play. The problem with such alternatives is that they'll be more cumbersome since they protrude externally and stick out like sore thumbs - which can cause a whole new set of problems.
My preference would be to keep the wireless internal (use the Mini-PCI).
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