Yes, there's a way to get back Windows 95 on your hard disk, but it is a big piece of a trouble because of the following reasons:
1) You only have the system files, and a boot disk. The best you could do (usually) is to start a system from the boot disk and try to recover the rest of your existed installation. From your explanation I concluded that you tried that and failed.
2) The Win98 started the installation process which lead to malfunction. This usually means that there's a number of corrupted files and misconfigurated pieces instead of your WINDOWS folder. Actually, this is the main your problem and I'll explain why:
It is not enough to have only system files and a boot disk. Because having those you'll be able to only *start* the system up, not work with it properly. Graphical interface files and all the programs and libraries are all there, away from your floppy.
That's why your only two choices are windows 95 or 98, but in either case you will have to reinstall them from the ground up.
Since you rejected the offers to recover and set up Win98, I would offer you to install a copy of the Windows 95 OSR 2, as the most known stable version. To do so you just boout up from the floppy (or use a bootable CD, if available) and rename the rest of your windwos folder into something like "windows.old". Then you may go on with the installation of the operationg system itself.
After some time you will get back your win95 system up and running fine, and will bestill able to recover some config files (if needed) from the folder of the "old" windows. After you are sure everything you might need is copied and backuped, you may safely delete the windows.old folder.