Hi Degrees. There should* a label at the base of the machine telling you month and year of manufacture. I have 2 machines with the black screen print on the front. One is 2001 and the other is 2003. My brother has the raised chrome Gaggia badge and it is a 2005 machine. I hope this helps.
Some site sponsors service the Gaggia Classics. One of mine was recently serviced by Di Bartoli and the cost is very reasonable.