Here's my solution. Use substr to extract the date part of the string and the time part of the string into two variables. Then use the input function with the mmddyy10. informat to convert the date string to a SAS date value, and with the time8. informat to convert the time string to a SAS time value.
Given a SAS date value and a SAS time value, the SAS documentation for the DHMS function explains how to combine them into a SAS datetime value.
Here's a data step to test my algorithm:
[pre]
data _null_;
input str $20.;
dtstr = substr(str, 1, 10);
tmstr = substr(str, 12, 8);
dt = input(dtstr, mmddyy10.);
tm = input(tmstr, time8.);
dttm = dhms(dt, 0, 0, tm);
put dttm datetime19.;
datalines;
10/16/2007 22:37:30
05/01/1953 11:15:27
07/04/1976 23:59:59
12/31/2000 00:00:00
run;[/pre]
Please test this for yourself to make sure it works.