On grml Linux you have to start with:
sudo apt-get update
sudo apt-get install gfortran

then start gamessmake.csh. Here's a log of the automatic compilation:

Building and running the current version of Gamess
in grml on i686
gamessmake.csh script version 2008-25-01
using gfortran v.4.3.0
TINKER, VB2000, NEO not enabled
 
01/25/08 12:37:48
making ddikick.x
......... finished
making gamess.00.x
......... finished
01/25/08 12:45:50
 
define SysV shared memory
kernel.shmmax = 400000000
run tests
finished
01/25/08 12:49:32
 
Checking the results of your sample GAMESS calculations,
the output files (exam??.log) will be taken from /home/grml/gamess/logs
All jobs terminated normally, now checking detailed numerical results
exam01: Eerr=0,0e+00 Gerr=0,0e+00.                                     Passed.
exam02: Eerr=0,0e+00 Gerr=0,0e+00 Serr=0,0e+00 Lerr=0,0e+00+0,0e+00.   Passed.
exam03: Eerr=0,0e+00 Gerr=0,0e+00 Derr=0,0e+00.                        Passed.
exam04: Eerr=0,0e+00 Gerr=0,0e+00 Oerr=0,0e+00 Derr=0,0e+00.           Passed.
exam05: Eerr=0,0e+00 Gerr=0,0e+00 Derr=0,0e+00.                        Passed.
exam06: Eerr=0,0e+00 Gerr=0,0e+00.                                     Passed.
exam07: Eerr=0,0e+00 Gerr=0,0e+00 Derr=0,0e+00.                        Passed.
exam08: Eerr=0,0e+00 Gerr=0,0e+00 Derr=0,0e+00.                        Passed.
exam09: Eerr=0,0e+00.                                                  Passed.
exam10: Eerr=0,0e+00 Werr=0,0e+00 Ierr=0,0e+00 Perr=0,0e+00.           Passed.
exam11: Eerr=0,0e+00 Rerr=0,0e+00.                                     Passed.
exam12: Eerr=0,0e+00 Gerr=0,0e+00.                                     Passed.
exam13: Eerr=0,0e+00 Gerr=0,0e+00 Derr=0,0e+00.                        Passed.
exam14: Eerr=0,0e+00+0,0e+00 Derr=0,0e+00+0,0e+00.                     Passed.
exam15: Eerr=0,0e+00.                                                  Passed.
exam16: Eerr=0,0e+00.                                                  Passed.
exam17: Eerr=0,0e+00 Werr=0,0e+00 Ierr=0,0e+00 Perr=0,0e+00.           Passed.
exam18: Eerr=0,0e+00 Werr=0,0e+00.                                     Passed.
exam19: Eerr=0,0e+00+0,0e+00.                                          Passed.
exam20: Eerr=0,0e+00 Xerr=0,0e+00.                                     Passed.
exam21: Eerr=0,0e+00 Werr=0,0e+00 Ierr=0,0e+00 Perr=0,0e+00.           Passed.
exam22: Eerr=0,0e+00 Gerr=0,0e+00 Derr=0,0e+00.                        Passed.
exam23: Herr=0,0e+00 Gerr=0,0e+00.                                     Passed.
exam24: Eerr=0,0e+00 Gerr=0,0e+00 Derr=0,0e+00.                        Passed.
exam25: Eerr=0,0e+00 Gerr=0,0e+00.                                     Passed.
exam26: Eerr=0,0e+00 Lerr=0,0e+00.                                     Passed.
exam27: Eerr=0,0e+00 Verr=0,0e+00.                                     Passed.
exam28: Eerr=0,0e+00.                                                  Passed.
exam29: Eerr=0,0e+00.                                                  Passed.
exam30: Eerr=0,0e+00 Gerr=0,0e+00.                                     Passed.
exam31: Eerr=0,0e+00 Gerr=0,0e+00 Ierr=0,0e+00.                        Passed.
exam32: Eerr=0,0e+00 Terr=0,0e+00.                                     Passed.
exam33: Eerr=0,0e+00 Gerr=0,0e+00.                                     Passed.
exam34: Eerr=0,0e+00 Gerr=0,0e+00.                                     Passed.
exam35: Eerr=0,0e+00.                                                  Passed.
exam36: Eerr=0,0e+00 Werr=0,0e+00 Ierr=0,0e+00.                        Passed.
exam37: Eerr=0,0e+00 Gerr=0,0e+00.                                     Passed.
exam38: Eerr=0,0e+00 Gerr=0,0e+00.                                     Passed.
exam39: RIerr=0,0e+00 HRIerr=0,0e+00.                                  Passed.
exam40: E1err=0,0e+00 E2err=0,0e+00 RMSerr=0,0e+00                     Passed.
exam41: EXCerr=0,0e+00 eV, Gerr=0,0e+00, OSCerr=0,0e+00.               Passed.
exam42: Eerr=0,0e+00 Gerr=0,0e+00.                                     Passed.
All 42 test results are correct!