Well seeing as everything with computers from hardware, software to networking evolves at a relatively high pace, it's not as much your static knowledge that counts, but really your willingness to learn, being interested and motivated. (And for support positions, your ability and affinity to communicate with people.)
Currently I'm working at the helpdesk of an automotive manufacturer that covers the entire country, the local main office and all locations (still as an external consultant but they've expressed interest in hiring me into their company). It's only a small team in this country so we nearly do everything ourselves which makes it very versatile and interesting. From handling first line inbound calls and mails to second line work on the hardware (including the servers, network), software installation, troubleshooting, to some third line tasks of testing software.
Just had a major project completed that involved working with colleagues in other countries but that could also mean more interesing work will move back to the country of origin. There's a few other big changes planned the next few months and I'm not sure yet how they'll impact my work.
Their plans for me, and my goals to evolve (be it there or at another company) is to fully immerse into second line support, development or team management. So I hope that turns out positive.
And as for support over the phone, we have software to take over their computers remotely, a big lifesaver.
If on Windows and you don't have Netmeeting or such enabled, check out
www.teamviewer.com, it's a nice, free tool for remote takeover that I've used privately as well.
but I fished a used copy of Persona 3 FES for 28 000 won.. I believe around 30 dollars or maybe a little less.