I have the higher end, two-speed, battery operated dremel that's not just for trimming nails. But every time I've seen it act that way it was (a) low battery, or (b) defective battery. If your dremel has been stored for years without use, you probably need to buy a new battery.
It's not the size of the dog in the fight, it's the size of the fight in the dog. Mark Twain