It was tried in the 1980s using nerve tissue from the Permian Basin Superorganism (PBSO). The computers actually made it to market, and were substantially faster than silicon on the market at the time. However, the cost and unreliability of maintaining life support for the biological components made them impractical for anyone except a few dedicated customers. By now, Moore's Law has well outrun what was capable with those early biocomputers, and since 2007, doing research with tissue from the PBSO has become substantially more difficult.

You can see a scan of an ad for the system here: https://bit.ly/3gYXs3v