What is the file type? .ACCDB or .ACCDE or .ACCDR? The latter two would depend on whether they contained code to actively disable notifications. If you are the developer, you would know if you had turned off notifications.
When the DB fails to open, there is little to do to determine after-the-fact that notifications were or were not enabled. But you said that with persistence, you could get it to open. IF you are the developer and it allows you to open the VBA coding page, then in the Menu Bar there is Tools >> Options, which leads to a multi-tabbed dialog that, on the "General" tab, selects how notifications are handled. If this isn't set to "Break On All Errors" then some errors could in theory sneak by - though you would not want this setting to persist once you have solved this problem.
There IS an odds-off chance that what is happening is a failure at startup. If you try to open the DB and it fails, IMMEDIATELY note the time of day. Then click the Windows Start button and start Event Viewer. Look in the System logs for an event at the specific time of day of the failed attempt. Events are sorted by date (by default) so it should be easy to scroll through and find something at that time - if it exists at all. If there is some kind of event for MSAccess.EXE as the primary failing process, look for the error or condition description. This is actually unlikely to go anywhere, but it is a non-invasive and relatively easy test, and you can safely back out of Event Viewer without changing anything.