With the exception of some ATX style-AT cases that were made during the transition, AT cases are completely incompatible. The AT case uses an AT keyboard plug (large circular), not the PS/2 used in ATX. ATX cases have a plate where the motherboard sticks all its connections out the back, while AT cases are missing the plate and instead have some serial and parallel port covers that can be bent out.
While if one looks really hard, one can find AT motherboards for newer processors: they are not mainstream. You will be much better off building a new computer from scratch than trying to use anything out of that machine. The possible exception of any modern PCI cards it might have. The Pentium 166 is a later modem Pentium and should have mostly PCI slots, the earlier Pentium 60, 75, and 90 systems generally had more ISA and/or VLB slots (along with a couple PCI slots) which would be of no use to you now.