A $30 phono preamp is going to get you at least $30 worth of problems. I'd at least get a Pro-ject PhonoBox Se or a Bellari VP129 and you will have at least $250 worth of pleasure.

I'm afraid the phono section of most receivers is nothing to write home about. My Yamaha RX-Z9's phono stage is ok but not great. But with respect to your problem; there should be enough gain in your receiver to drive an MM cartridge, and you may have a fault in the receiver itself. Perhaps a call to the manufacturer's service center is in order.

There's possibly..apparently..a bit of a joke hiding in the name of the Cambridge phono pre.

You see, digital can be equated, to a certain degree..to 'interlaced' video signals.

'progressive scan' can be considerd the TRUE analog (film frame) version of the signal, comparatively speaking. Full frames instead of the interlaced 'faked progressive scan' version, with far less data.

In the UK, they use PAL as a video base, in this case, the two formats are:

540i..interlaced video, and
540p..progressive scan video.

Analog, true progressive scan, etc.

Just thought you might like to know that the Cambridge guys might be having an unannounced funny.

And if they have a tiny little ~$100 DAC, it might be called the '540i"

If you can barely hear the turntable at normal levels, it sounds like you have a low output cartridge and you are not getting enough gain from your phono pre-amp. Phono pre-amps can be high gain or low gain. Some have a switch the adjust the gain. The nicer cartridges are generally low output, but require a high gain phono stage.
I think you should check the output of the cartridge and the gain of your phono pre-amp. Go in to a good audio store and let them help you.
Good luck.