I share some of SD's concern about SATA vs IDE..
My inclination would be to install the new big drive as drive D, and move all non-software stuff from C: to it. Assuming your 35GB isn't chock-full of software, you should find you can free up most of it.
Changing the address of your "My Documents" file to D:\Documents is not difficult - that will automate the process thereafter.
My machine (for long, boring historical reasons allied with apathy to change it all) has drives covering most of the alphabet. Drive C is 20GB, with about 7 GB free. It has a total of 800GB, that lot about half full.
If you have the installation software, you can even uninstall non-Windows software on C and reinstall it to drive D.
If you're worried about Drive C's age, buy a decent-quality IDE drive (80GB would be more than enough) and clone the existing Drive C to that.