Surging as though I was trying to move with handbrake on

It has been about ten days since my car was driven due to Christmas holidays. Today I got in my car, turned on the engine, put in reverse to get out of car park, released handbrake and the car would not move. Was surging as though I was trying to move with handbrake on.
Put handbrake on, put into first gear, released handbrake same problem, car surging as though trying to set off with handbrake on.
I decided to give it another go, but into first gear, released handbrake, car surging as before, kept foot on accelerator, after two to three seconds maximum there was a loud mechanical bang/clang noise and car moved forward.
I tried it a couple of times more in both first and reverse and car moving backwards and forwards normally.
Drove to shop and seemed to be driving okay except when braking there is a very gravelly type sound. I am pretty sure my car brakes have sounded like that after not been driven for a while in the cold/damp before though and I am just been paranoid!

Does this sound like something dangerous that I should be taking my car to be looked at for?

Thanks for any advice.

Julie