I'm currently running Mint 11 with kernel 2.6.38. However, I have hardware that requires an older kernel (2.6.18 or earlier).
Is it possible to compile and install an older kernel for use in my current installation of Mint?
In principle there is nothing to stop you downloading an older kernel, configuring, building it and its modules, and installing it.
However it is likely you will break something else. It is likely that there are kernel dependencies in other parts of the system - graphics drivers, X modules, sound systems etc.
It is also likely that Mint's kernel deviates from the standard kernel.org kernels, and there are dependencies on those deviations.
If any of your other hardware wasn't supported until after 2.6.18, it will not work either.
Anyway, perhaps the best bet is to try.