Based on your saying that all of device buttons flash at the same time I think the remote is broken. There is no way I know of for the DVR to make that happen. Do you have a remote for another FiOS STB of any kind available, or does a friendly neighbor have one you could borrrow? If so, try that remote with the DVR; if all works OK then it is definitely the original remote. All FiOS remotes should work with any STB.
Once you verify the remote is the problem you should be able to contact the FiOS FSC (1-888-553-1555) and request a replacement, they should ship it to you in a day or two and there should not be any charge. If you get frustrated with the automated phone system you can say "agent" at each question and it will usually get you to a live person pretty quickly. And you can call 24/7 for help.
My experience with the FiOS remotes is that for some reason they need to be really accurately aimed at the DVR to work, at least at times. I cannot explain it, but sometimes the DVR just will not respond unless the remote is really aimed directly at or above the DVR, other times it will work just fine aimed way, way off - a mystery to me. I can take the same remote to either of my other STBs (non-DVR) and it will always work just fine, doesn't have to be aimed carefully, etc. So it is not the remote, it is the DVR.
Hope this helps.
Verizon FiOS TV, Internet, and phone
QIP6416, IMG 1.6.2, Build 08.58
Keller, TX 76248