Magento – No Orders in Reports > Sales – Orders

Sounds like Magento's cron is failing for some reason on the server. I'd try manually running the cron script and monitor the PHP error log and Magento Exception log, or using a tool like n98-magerun to manually run individual cron jobs and see what sort of errors happen.

2 issues may be here,

First the timezone one - There’s been an issue for some time with the date pickers in the admin screens being in inconsistent timezones. Internally everything is saved to the database in Universal Time (essentially GMT) and the user facing elements such as date pickers and report results should be shifted to your locale’s time, however some actions haven’t been caught so you’re actually getting GMT based results in some cases.

The bigger issue for reports though is refreshing the statistics. Try hitting

Report > Refresh Statistics

and refreshing them all manually and see if it’s still wrong. Even though the last updated dates look right for me and all cron jobs appear to be working I find I get these same errors unless I do this.