Yea it needs its caps replaced. It's been like this since about 2002. Just gonna get a sound card instead, as money's too tight to mention.
What amiga is it? I just did my A2000 with an ok soldering iron, desoldering braid and flux. I am still waiting to do my A4000 because of the surface mounted style (I have been told desoldering air gun the only way to do it safely). Cosmos would know, but if its an A1200 I bet it has those SMD jobs like the A4000.
EDIT: Its an A4000. I'd definitely invest in getting them replaced. the ones on my 4000 in the audio section are leaky and have discolored (IE eaten at) the legs on a nearby chip and my sound channel is still good.