We report on measurements performed at low temperatures on a nanoelectromechanical system (NEMS) under (capacitive) parametric pumping. The excitations and detection schemes are purely electrical and, in the present experiment, enable the straightforward measurement of forces down to about a femtonewton, for displacements of an angström, using standard room-temperature electronics. We demonstrate that a small (linear) force applied on the device can be amplified up to more than a 100 times, while the system is truly moving. We explore the dynamics up to about 50-nm deflections for cantilevers about 200 nm thick and 3 µm long, oscillating at a frequency of 7 MHz. We present a generic modeling of nonlinear parametric amplification and give analytic theoretical solutions enabling the fit of experimental results. We finally discuss the practical limits of the technique, with a particular application: the measurement of anelastic damping in the metallic coating of the device, with an exceptional resolution of about 0.5%.