Does the Sallen-key filter require a buffer for low power applications?
Your issue is probably noise. You should start by calculating the thermal noise voltage in 10kHz bandwidth @3.4kohm, and deciding what signal/noise ratio you need to get. That will probably tell you that you need a low noise preamp/buffer before the filter.

An active filter is very noisy. You have R1,2,4 all adding thermal noise. You have the input signal attenuated by R1C1 R2C2. Then you have opamps which are mostly fairly noisy. To get the thermal noise voltage down, you need to make the R's much lower than your source R - which means you must buffer. But it also means that you need an opamp which has a low equivalent noise resistance. The best opamps (AD797) have about 500ohms ENR - so you can't make the filter Rs much lower than this or again, noise figure gets worse.

This active filter arrangement is noisier than one which has only a single RC per filter stage. If you put OA2 before OA1 (with gain) it would be the preamp, and the whole would be quieter.

If you have out of band signal that needs filtering before the preamp, an LC low pass filter would be best. You will need a preamp before the active filter, with significant gain (40dB / 100x) to get good SNR. LC filters are well worth considering. This whole arrangement performs worse than one L and 2 C's.