What reason do you have for disconnecting the battery?
It's beeping because it thinks the battery has a problem -- and it's right, you unplugged it.
Hook the battery back up. If it needs replacing, call Verizon and they're supposed to take care of that (so our installer said) because it's technically their equipment.
Also, the battery backup acts as an uninterruptable power supply for TV and Internet -- it will provide protection against momentary blips and brown-outs. Also, if you get a battery backup (aka UPS or Uninterruptable Power Supply) for your computer and the FiOS Router, it will give you 5 minutes of TV/Internet runtime after the power goes out. Verizon may dispute this claim but I've tested it so I can tell you it's true.
EDIT: Ok, sorry I didn't realize the battery was bad. You could try and see if the "Silence" button (if your model has it) on the battery unt does anything but I doubt it will. Short of breaking the case open open and physically cutting out the beeper or it's wires, I'm not sure there is any way to disable it.
I'd call Verizon again, maybe you'll get a different tech that's more helpfull. Tell them that the original installer said that Verizon would maintain their own equipment, see if you can get them to replace it for you. Try telling them you can't afford a battery to fix *their* equipment, see what they say...worst they can do is say no.
If all else fails, don't go to RadioShack -- I like them for hard-to-find things but this isn't one, and their prices on batteries are quite high. Lowe's/Home Depot probably sells alarm system batteries which should be compatible (bring the old one to compare voltage/amperage/physical size) or if there's a Batteries Plus ( http://www.batteriesplus.com ), they specialize in hard-to-find batteries.
When looking for a similar battery, the Voltage MUST match exactly, the amp-hour rating (Ah or mAh) should be equil or greater than the original, and the connecters must be the same type. Anything that meets those three requirements and physically fits should be ok to use.
EDIT2: I found this on Verizon's site...still worth calling and ask if there's a way to override or circomvent the battery alarm...
"Customer is responsible for backup battery replacement. Important Note: The Verizon supplied battery is designed specifically for use with the Verizon FiOS Network. Use of a battery other than a 12-Volt 7.2 Ah SLA Sealed Lead Acid battery is not recommended since other battery types may impact the performance of your FiOS services. Verizon is not responsible for damages which result from use of an improper battery. Certain telephones, answering machines and other telephone equipment not meeting industry standards may not work with service provided on the Verizon FiOS network. ©2009 Verizon."
Here's a list of batteries from BatteriesPlus, the store near me has the first one on this list for $30 + tax (+maybe shipping if you don't have one nearby).
http://www.batteriesplus.com/Search.aspx?searchterm=12v-7AH
It's a common enough battery that most places who sell alarm systems will have one -- and it's similar to batteries used by some self-powered toys (scooters, Barbie cars, etc) and a few self-start push mowers so you could check places that carry those things. Anywhere would be cheaper than RadioShack for this particular item.