That´s right; "my computer dropped out of Internet or dropped the connection." would do (let´s say, with a slight focus on the PC itself) and "the connection dropped" (with focus on the Server or on the PC; in other words, not specific).

Ah, in these days of wireless and cell Phones, they may drop the connection as well (I am talking about the ones with Web access).

I hope you fix your computer´s drop outs in 2010 CR!          ;- )

PP.