If there are no transaction log entries, then likely PayPal isn't even hitting your server. You need to look at your IPN configuration within your PayPal account and confirm that they're enabled.
Unfortunately, if IPNs aren't enabled, then there certainly isn't anything that can be done retroactively. You'll need to use the manual upgrade options within the XF control panel. If IPNs are enabled, you should be able to view the IPN history, which should confirm the URL PayPal is hitting and the response it's getting.