is it possible to copy some files I would like to keep from my old hard disk with win 98 op system across to the new disk
Yes definitely - the files will copy across.
If they are photos, documents and spreadsheets, etc then no problems.
If they are software applications then as others have said above it depends on the individual applications as to whether they will just run, or whether you would be better off finding the original CD/floppy/download URL and reinstalling.
RC