If you want to keep running after one disk fails then you need at least one more disk with the same data on it, and a transparent way to access a shared device which manages the data on both drives. That comes down to:
- Hardware RAID. (Usually expensive and the RAID card should not die)
- Software RAID. (Not sure how this works under windows)
- Fake RAID with the motherboard. Basically this is software RAID but with support from the BIOS or UEFI and often limited to the same generation of motherboards.
To archive what you want I would advise HW RAID, except that you specified without HW RAID if possible. The next best thing would be SW RAID or fake raid with a spare identical motherboard.
A last option would be not to use RAID but keep a daily backup of the drive containing c:\ in a different drive. That would require rebooting (and pulling a broken drive) after the primary drive containing your c: volume dies, but it involves the least hassle to set up. This edges toward some kind of backup, which is also something you did not want. Basically this confuses me. (Do you already have backups and want to avoid those in the post?)