What /\/\ he said. I very much doubt a 2004 bike had an intergrated head set. Much more likely to have an integral (aka zero stack) Head set.
Have a look here
https://www.hopetech.com/_repository/1/documents/HOPEHEADSETS2011Web.pdf
Using the above document measure the frame, I’d guess it will measure 44mm top and bottom. Which is hope No2 or zs44 (zero stack 44mm) what you have tried to fit is an Is41 or hope No3 which is 3mm too small which would explain why it might seem loose or worn.
for what you want the bike for Plenty of options on eBay for about £10 search zs44
Obviously this is speculation currently but if you upload a pic it will hopefully become clearer.