There's a big difference between the buttons being 'faulty' because of an actual physical failure or simply because they're not responding to whatever you're trying to do with them. And it's more common to have the latter problem than the former. Did some accident occur where the phone was damaged in some way, which could have involved the buttons also being mechanically damaged? Or have one or both been a problem recently? If not either, odds are the buttons just aren't responding, which involve a software-related issue. It's also a bit of a mystery as to how your phone ended up in its Download mode. Please elaborate. Did something occur where your phone just rebooted itself or did this happen when you rebooted it for some reason?
Have you tried just starting your phone by holding down the Power button for several seconds? (don't be surprised if it takes 10-20 before anything happens)
If it does and restarts normally you should be OK but if you do have a lot of data saved on that phone, it's really, really important to implement some kind of backup solution. Really, backups are important.
If it doesn't and just starts up back in its Download mode again. That's not a good sign. Typically when an Android device just gets stuck in a boot loop into its Recovery or Download mode, that's an indicator the installed Android operating system has been corrupted somehow, bad enough that the phone can't start up normally. Trying to fix this problem and save your stored data over any online help forum isn't likely to be work out for you. Take your phone to a trusted, local service shop to have them look over and access the situation. Be sure to emphasize you have important data you need to have saved.