gcminer with ATIRADEON HD3600 on ubuntu 12.04 64bit headless won't detect GPU
OpenCL is not supported on 3xxx series cards.  Although it's not completely impossible to mine on a card that old it will be very difficult.  Also, a card that old will produce less than 1 MH/s which will only be fractions of bitcoins.  I wouldn't waste my time fighting the Radeon 3600.

If you are serious about mining check out the 5xxx and 7xxx series cards.  Or better yet, look into ASICs.