Hi. Have you tried increasing the capacitance? The added series resistance should also cutoff the amplification over about 100KHz, in case your cable is picking up interference, even if your amp losses amplification: it is optional, and if you are not that worried about pickup, could be removed / reduced (try with a pot).
Project 13 as linked by PeterFW is a beautiful preamp, similar to yours (note R=1.2K and C=10u at the input of the first transistor, though in yours I'd place the resistor just at the base, for better gain), but with very clever multiple feedback going on. If you can adapt this circuit to your 5V (I guess) supply, it will beat the open loop design in all respects.
I'm not sure what do you mean by digital signals: is it Morse code, low baudrate digital audio, or what.
Just to clarify what do I mean by high pass filtering, I will attach a spice simulation of the preamp. It confirms most of the calculations I did by hand, with a little variation in bias (I assumed beta=100, that's low for a 547B).
The file preamp.png is the circuit as described. In gain.png you can see its frequency response: the gain rises at 6dB per octave below 1KHz; low frequency input is very much attenuated compared to higher frequencies. In squre_resp.png you have the output for a 10Hz square wave in this amplifier: you only hear the steps as a series of clicks. Could that be the motorboarding?
The file preamp_new is the improved version. In gain_new.png you have its response: you lose 6dB due to the resistor, but gain starts to decline at about 100KHz, if RF pickup is a problem. Remove the resistor if it isn't, you'll keep the gain, up to HF. Square_new.png is the amplification of the 10Hz square wave, far from optimal, but at least adequate.
I hope this helps.