Can I control the Verizon Fios cable box with a regular TV remote?

Not likely. Cable and satellite receivers and DVRs (including FIOS) have a number of unique operations that cannot be controlled by a 3rd party remote. You need to figure out what's wrong with yours and get it fixed or replaced. The remote belongs to Verizon, so I'd start with their tech support. You might get advice on how to bring yours around, or maybe even a free replacement.