Decoding waveform from RFID 125 khz reader
I think the AC coupling high pass filter rolloff frequency is too high, and is getting in the way of the data.  It looks like your second attempt, which uses C19 as intended, worked better.  Try again with both C3 and C19 increased.

Everything to the right of C3 in your schematic is just a amplifier, and a not particularly good one.  Try removing everything to the right of C3 and connecting that to your sound card input directly.  You may need to use the "microcphone" input due to the low signal level.

It would be useful to look at the right side of D1 with a scope to see what the raw signal really looks like.  Once you know what you're starting with, it shouldn't be too hard to design a amplifier and data slicer for your signal.  But, without knowing the specs of the input signal, that's going to be hit or miss at best.