With just a web browser you can open an account at bitcoinmarket, mybitcoin, or mtgox and send/receive bitcoins.
The only thing you're not able to do is try to generate bitcoins, but you said you don't have a computer at home and it sounds like your employer wouldn't be very... uhh, supportive... of you using their electricity to try to generate bitcoins.
If they would be supportive (long ago I wrote software at a hardware company where they actually LOOKED FOR CPU-intensive applications to run during system burn-in, so they'd ship fewer dead-shortly-after-arrival units) then they'd probably be happy to open up outbound connections to port 8333.