The core part (descriptive summaries and simple maximum-likelihood estimation) of the Timepath program will (and has) run fine (and quick) on a circa 1982 8088 machine. The use of bootstrap resampling to provide the much-needed assessments of uncertainty for the parameter estimates does place greater demands on the computing facilities.
The so-called architecture of the program writes the results of each bootstrap resampling to disk on the same directory as the *.exe file and then sorts and summarizes at the end of the resampling. In light of this, the way I run this program (when using the bootstrapping) is to create a large RAM drive (4 MB should do; I never have tried to figure the minimum size), copy the data and the *.exe file to this RAM drive, and then after program completion copy the output files etc back to permanent storage. The purpose of this RAM drive maneuver is to avoid the slower writing/grinding of your hard drive.
On my circa 1991 33Mhz 80486DX machine, the Table 2 artificial data run used as the example here with 4000 bootstrap resamples takes about 4 hrs 20 min. So a mid-range 1995 machine could do all this in under a hour.