Those old 600 series Ultegra parts can literally last forever if treated properly: I know, I toured all over eastern Québec in 2003 and 2004 with an old Nishiki that had the very same component set. The wheels were junk, the bars were rusty and the brakes were worn to nil, but the downtube shifters and brake levers, as well as the derailleurs worked perfectly.

Keep your old rig for fun, and maybe look into something newer, maybe a nice Bianchi Via Nirone?