I regret that I am not able to figure out your design structure from the additional information that you've provided.
I doubt that two blocks are defined by the two conditions. Blocks are typically considered to be random effects factors which determine the variance of the response and do not affect the mean of the response. I believe you are thinking of condition as a fixed effects factor; if condition is a fixed effects factor, then it cannot also be a random effects factor. So you'll want to think more about your design structure.
Blocks are clusters of experimental units: units within a particular block are assumed to be "similar", and units between blocks are assumed to be "different". You may have clustering in your experimental design, or you may not.
Design issues can be complicated, so if there is someone at your institution who could help, I suggest talking with them. There is, of course, a lot of books, papers, etc. on the topic of design.
Or you could try again here, with a lot more detail about how you ran the experiment.

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