Nikon D60 in very low light?

I wanted to shoot a very clear, starry sky. I set the camera up on a tripod, set the camera to all manual settings, and used my remote release. I opened the aperture all the way and set the shutter (at first) to 30". The camera kept indicating "low light" and would not release the shutter. I then tried the bulb setting with the same result. I have taken these types of photos before with success on my old 35mm. There were two photos I wanted: one of the milky way and then an extended shot with the stars creating swirled lines (for a lack of a better way of describing it) - the latter I would have set the shutter for at least a couple hours or so. How can I get my camera to take shots like this?

Since you have worked with 35mm film the question I'm going to ask may sound like an insult. Did you actually open the aperture fully? Low number such as f3.5 or f2.8? (That would fully open the aperture) Not large number such as f11? (That would nearly close the aperture).

The camera would indeed indicate low light, since the overall quantity of light was small, but all you wanted was the starry dots, and the camera can't know that (it was looking mostly at the dark sky between the stars).So fully Manual operation of the shutter was dictated, and indeed you used 30 seconds and Bulb. At Bulb the shutter stays open as long as you hold the button, so did you hold it for longer than 30 seconds?

Even at 100 ISO something of the brighter stars should have recorded at aperture f3.5 at about 30 seconds. Try raising the ISO, but not above 400 so as not to get a grainy sky.

It may have been refusing to take the shot because there was not enough light to auto-focus properly. It might not let you take the picture if it can't focus in AF mode. Put the camera lens into manual focus mode and try again. It "should" allow you to take a shot in manual focus mode whether or not it thinks focus has been achieved. If necessary try changing the MENU > Custom Setting Menu > 02 Focus Mode on the camera.

I used to find the D60 was fine up to ISO 800 so see if that helps as well.

I agree, the impediment is that the autofocus had nothing to lock onto. Alas the kit lens has no distance scale. You can try pointing it at a distant street light, or you could maybe point you car's headlights at something to get it to lock onto a close to infinity focus, and then switch it to manual focus.

Switch off auto focus and focus manually. Make sure you are on fully manual exposure.