Hmmm... let's clarify the things a little.

There are several pixel diseases which can lead to this behavior:

Dead (sub)pixels - A dead (sub)pixel is a permanently damaged (sub)pixel that does not receive any power. Mind you, because we're talking here about a RGBG (Bayer) sensor here, the resulting color can be different from black if only one (or two) subpixels are dead. That's why the dead pixels do not normally show up as a black spot, but will rather show up of different color than adjacent pixels, or will be slightly darker than adjacent pixels. This is (of course) an QA issue, is permanent, and cannot be fixed, except, of course, by replacing the sensor. That's why dead pixels are rare on digital camera LCDs and sensors – manufacturers typically take care of dead pixels during their extensive Quality Assurance (QA) process.

Stuck pixels - Compared to dead pixels, stuck pixels always receive power, which results in a colored pixel that shows up in the same spot on the image. The colors can be red, green, blue or any combination of these colors. Unlike dead pixels, stuck pixels do not change their color from picture to picture. Stuck pixels are very common, but not permanent like dead pixels – they might disappear overtime. To find out if you have a stuck pixel on your camera sensor, take multiple different pictures at a base ISO such as ISO 100 or 200, then analyze the images at 100% on your computer screen. If you have a colored pixel (actually a small cross when viewed closely) that always shows up in the same spot, you have a stuck pixel. How to fix: either pray to go away either going to a Nikon service center to replace the sensor either both.

Hot pixels - Unlike stuck pixels, hot pixels only show up when the camera sensor gets hot during long exposures or when the ISO is cranked up above 400-800 (for your model), or even higher, depending on the camera. Hot pixels are very normal and they will show up even on brand new cameras, although manufacturers do their best to map hot pixels out during the QA process. Hot pixels will appear and disappear overtime (depending on sensor temperature) and it is a very normal thing to have them, even for the newer models the things are getting better. How to fix: cool down. Don't shoot too often long exposures, (if you'll have a camera with Live View) don't use too much Live View. Shooting in cold environments will certainly help, not only in the problem of the hot pixels but also in the matter of high ISO noise.

Because you're saying that

either in Day light or night shot...

...I assume that you don't work with long exposures in Day light and hence you have most probably some stuck pixels (or perhaps dead). One solution is to fix them in post-processing for each photo. But if you cannot afford this, then you must change the sensor but for your camera I'd recommend better to change the entire camera. Nowadays, the price/performance ratio for a new camera is waaay better than for yours which it is a quite old one.

In short: Generally, I'd recommend upgrading your camera to a newer Nikon model in order to keep your lenses. If you have indeed hot pixels and you don't have the possibility for a new camera just be more patient, don't shoot too often and wait for the sensor to cool down.