Dropped my sony digital DSC-W370 14.1 and the lens would not close. Have taken it to camera repair shops but they want to charge more than I payed for camera. Would like to know if I can try to close lens without paying a fortune. Lens not broken just a little dent on cover.

The lens error is due to failure of the lens control system. You can remove battery and card replace battery and while switching on tap the lens hood on your hands so as to disengage any dirt or mechanism being struck.
Use some air to blow between the lens to dislodge any sand particles struck inside. If none of these works then you can think of taking consensus with the service center on a reasonable estimate as some of the costs are high and hence they charge more.If the get estimate is high then you decide to scrap and go for a new model.Since some of the spares are available only with Sony service, this must be thought of, as you do not have to run around for spares.
However if the camera works without the lens shutting try and use it without any repair as Sony would have estimated for lens mechanism assembly