If you have a command like this:
* * * * * /path/to/script >> /tmp/outputand it doesn't work and you can't see any output, it may not necessarily mean cron isn't working. The script could be broken and the output going to stderr which doesn't get passed to /tmp/output. Check this isn't the case, by capturing this output as well:
* * * * * /path/to/script >> /tmp/output 2>&1to see if this helps you catch your issue.