Multiplying 10 times with opamp
Your final opamp (U3A) is wired correctly for positive gain.  With the resistors you show, its gain will actually be 11, not 10, but that's not related to the problem you are observing.

So what to do?  Start debugging, obviously.

First verify the signal at the output of U2A.  From your description, it seems that is as expected.  OK, so keep going.  What about the right side of C1?  Does that make it to the positive input of U3A?  Check right at the pin.  Don't assume the connections are correct and working.  If the signal is at the positive input of U3A, what's on the negative input?  It should be the same signal.  Then check the output.

Again, this kind of diagnosing really should have been the obvious thing to do.

If everything is built as shown by the schematic, then one problem may be the frequency of the signal.  Saying that C1 "blocks DC" oversimplifies it.  C1 and R8 really work together to form a high pass filter.  In this case, the rolloff frequency is 160 Hz.  Is your signal lower frequency than that?  If so, that explains why you're not seeing it on the output, or why it is more attenuated than you expect.

If you replace R8 with 10 k&Omega;, for example, then the high pass rolloff frequency goes to 16 Hz.  That also puts less of a load on U2A.

All the above is assuming the LM358 is used correctly.  You didn't link to a datasheet, so I didn't look it up and check any of that.