I gave it a listen and can hear what you're talking about. Before we start pointing a finger at Broadcastify, let's try a few things.
Can you hear the background noise on your scanner with headphones?
Does your HP All-In-One have a line-level input? If so, try using that instead of the USB audio card and see if you notice a difference. It is possible that the USB audio interface is introducing noise into the audio signal. I once had a USB interface that was horribly noisy ... that interface was quickly replaced.
Have you tried a different audio cable between the scanner and the interface? Some cables are low quality and can introduce noise.
Using this free meter software:
Audio Level Meter
try to set your maximum volume level between -8 and -4 by turning up the scanner's volume and turning down the line-level or USB interface volume. This will reduce any noise being introduced by the computer (some computers are very noisy) and may show that the noise is being introduced by the scanner, the audio cable going to the interface, or by the interface itself. The All-In-One may be part of the problem itself, generating some of the noise internally, possibly from the screen backlight.
Can you try it on another computer altogether, one that is not an All-In-One?
Is your location in close proximity to towers? If you are close to a tower or towers, there may be some signals which are extremely hot and bleeding into the scanner (I once had this problem with a paging service, until the service adjusted its transmitter). Have you tried the scanner's global attenuator to see if that helps knock down the noise? If it does, then I'd suggest trying the attenuator on a channel-by-channel or trunking-site-by-trunking-site basis to see if it eliminates the noise. It may be that you'll have to try it on multiple frequencies to isolate and remove the noise.
Noise problems can be tough to track down. It may turn out that a number of small solutions will resolve the entire problem.
Please try these things and report back.