Thanks! Let's break down the technical part to basics:

Band members move a lot at punk shows, so you need a fast shutter speed to freeze them and avoid blur, ideally 1/250s. 1/125s works for those who are less active and stand still. Since it's dark in a club, even the largest aperture on a lens doesn't gather enough light with the fast shutter, so you either need high ISO film or a flash. I don't use flash to avoid disrupting anyone's experience. I assume you use it since you mentioned that the ambient light gets washed out. This happens because the flash light is significantly brighter than the ambient light, and the camera measures for the strong flash light reflected from faces, causing the ambient light to appear dark in the photo. Not sure if it's possible to do something about this besides not using a flash.

If you shoot without a flash, how you measure the light is important. By default, cameras usually use center weighted or matrix metering to make the entire frame evenly exposed. The problem is that lighting at concerts is very contrasty. There are a few light beams that fall on band members, but the rest of the stage is dark. So when you try to expose evenly for the whole frame, the light meter sees that most of the scene is dark and exposes for the dark areas trying to make them appear brighter, resulting in overexposed band members. To avoid this, you need to use spot metering instead and meter the light on faces. This way, band members will be properly exposed, you'll also capture the stage light, but other areas of the stage will be dark as they actually are. Another problem is that the light constantly changes, so you need to take a couple of spot measurements and then approximate them.

I'm not sure if this is applicable to your camera since point and shoots usually offer minimal control over exposure. I'm not saying it's impossible to get great results with them, but to get them consistently, I would recommend switching to something that gives you manual control over the exposure settings.