Possible bad news:
 Make sure you get the replacement right. The frist ST's ('97) ran on a unique charging system (400W) from Ducati which only lasted a year before being re-designed (450W) - probably because it was pants.
 
 Possible good news:
 Talk to Duccati UK. They may pay for free fitting of a new one as they know how bad the system was. I doubt there are many originals still running out there. 
 I know this sounds far-fetched for such an old bike, but they paid for mine when the bike was 7 years old.
 At the same time, check that there are not any re-calls still outstanding on your bike (use the chassis number). There were 3 or 4 for these models and 2 of them were important.
 
 Regards,
 Mike