open ACCESS, ">> $log" || die "Cannot open $log: $!";
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open ACCESS, ">> $log" or die "Cannot open $log: $!";
#or
open (ACCESS, ">> $log") || die "Cannot open $log: $!";
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open ACCESS, ">> $log" || die "Cannot open $log: $!";
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open ACCESS, ( ">> $log" || die "Cannot open $log: $!"; )
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1) Your || has too high precedence.
open ACCESS, ">> $log" || die "Cannot open $log: $!";
is equivalent to
open ACCESS, (">> $log" || die "Cannot open $log: $!");
which is equivalent to
open ACCESS, ">> $log";
Instead, use
open(ACCESS, ">> $log") || die "Cannot open $log: $!";
or
open ACCESS, ">> $log" or die "Cannot open $log: $!";

2) You don't check if chdir succeeded.

3) The three argument form of open is safer.

4) Using lexicals for filehandles is cleaner.

5) The following is easier to read and less error-prone:

my $log = $file;
$log =~ s#^.*/##;
$log =~ s#\.[^.]$##;
$log .= '.log';
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6) join might be a better choice instead of all those string concatenations.

7) Finally, you could eliminate the chdir as follows:

$log = "/perl/web/examscores/$courselocation/access/$log";
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Fixed code:

    my $clocktime = localtime;

    my $log = $file;
    $log =~ s#^.*/##;
    $log =~ s#\.[^.]$##;
    $log = "/perl/web/examscores/$courselocation/access/$log.log";

    open(my $access, '>>', $log)
       or die("Cannot open $log: $!\n");

    print $access (
       join(' ',
          $idinput,
          $lname,
          $fname,
          $clocktime,
          $useripaddress,
          $time,
       ), "\n");

    close($access);
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By the way, localtime returns a string with spaces in it (in scalar contect).

I would check what your value of $log[0] is. You may be making a logfile -- just not the one you're expecting. Also better clarity in your variable naming wouldn't hurt. $logname might be clearer than $log and avoid confusion with your @log array.

If you are still not creating a log file check the permissions on the directory into which it is trying to write. chdir may not be your cwd so your log may be printing somewhere you don't expect. ( Like where you are starting the script from )

One last suggestion would be to simplify the setting of the logfile name with 1 line $logname= "$log[0]\.log"

use strict;
use warnings;
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Chris.

First, use the open( ... ) form of the function.. given the issues with operator precedence it would be very wise to use the parenthesis (also known as brackets).

Second, if your server is rebooting I highly recommend pulling out the debugger. perl -d<script>. Then single step through each line until you hit the one that makes your server reboot.

If you're using CGI through Apache and don't have the option of running a debugger, then one approach you might take to finding the line causing the issue is sprinking sleeps and debugging statements.. e.g.

  $| = 1; # turn on autoflushing of print statements
  print( "<p>About to open file..</p>" );
  sleep( 5 );
  open( ... ) or die( ... );
  
  print( "<p>About to append to file..</p>" );
  sleep( 5 );
  print FILEHANDLE $statement;

  ...
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and soforth..