Leaf Blowers

I bought a Weedeater LB 20V rechargeable leaf blower in 2012. Recently it started cutting off after about 30 seconds, then will only run by constantly switching to "off" and back to "on". Took it to be serviced, and for $20 was told it was probably in the coil and not worth fixing. Bought a new one($40 for just the hand-held part)which does the same thing as the original(using the "old" battery, which registers as fully charged). Is the battery the problem? or the charger? A new battery costs around $55, so I would like to know if this is a common complaint before I buy a new one. Thanks