My Pentax K100 DSLR is flashing "av" and will not take a photograph, though the shutter works fine and takes pictures without the lens.

Sounds like your shutter is stuck. Given that the camera is only worth about $100 -- or even less -- it's probably not worth sending in for repair. You can buy a good used "upgrade" like the K200 or even the K-50 for about what a shutter replacement would cost.

Assuming you are familiar with the setting of your camera and have used it without issues in the past, the camera should be professionally cleaned & serviced by Pentax or reputable camera repair shop.

It is likely that dirt or oil has begun to interfere with proper shutter operation, or that the end of shutter's life is approaching. If under warranty still, be sure to have only Pentax or one of their authorized agents perform this work or risk voiding the warranty. Regardless of warranty state, this is a replaceable part (if cleaning does not solve the problem) on most dSLR cameras, but may be expensive. Be sure to specify that an estimate is provided before work is commenced - or provide a dollar amount that you are willing to pay.

You can arrange for service by Pentax on this page.

I hope this helps and good luck!

Try cleaning the contacts on the camera body and lens where they meet with a cotton swab lightly dampened with rubbing alcohol.

You can't.

In Auto Pict mode the camera selects the best of the pre-set Scene modes for the photograph which you're about to take. It's basically a variation of fully automatic mode, so the camera selects everything for you.

Auto Pict and Auto are designed to let anyone pick up your camera and take a fully automated snapshot without needing to worry about what settings to use.

To alter the shutter speeds you need to select an appropriate mode such as shutter priority or manual.

Any Pentax K-mount lens will fit any Pentax DSLR. The DSLR will fire the shutter.  There is a menu setting (RTFM) which allows the use of older lenses, but you will lose some of the automation (again RTFM). Remember to allow that the effective focal length when using a "film" lens on a DSLR body goes up by 50%.
A standard 50mm lens becomes a 75mm equivalent, but stays a large aperture.

I've got the same problem. The problem is that the lense is loosely attached to the body. What you need to do is that when you see the Av flashing, press the lense of the camera to the body and twist the lense to the left a bit. This tightens the connection. You can then take the photo.

just set the shutter speed yourself. and unless its on a tripod it wont be steady enough.

is it set to auto? if not i suggest you check the aperture and shutter speed setting :)

Might be temporary lack of communication between lens and body - try cleaning the contacts on both gently with a lint-free cloth and a very little IPA.

The lenses are probably manual focus lenses,  

1. Make sure that the apature ring is set to 'A' or automatic, 
   
2. if these are manual focus lenses then switch the focus switch on the left side of the camera body to MF 
3. If this still doesn't work, or you are having trouble with the apature ring then press the menu button to go to the  menu then press the right arrow key untill you are in the  Custom Settings, scroll through the custom settings with the up and down arrow keys until about the 2nd from bottom there is an option called "using aperture ring" set this to 2 (Permitted) This will make the camera take a image when lens is on any f-stop manually. 

Try this and everything should work fine. If all this hasn't worked then try seting the mode dial on the camera to M manual mode. Cheers