multi-condition left join conditions in MS access
Are the tables you are querying indexed?

If not, I would add an index to the "Inv.SN=Dep.SN"columns ,
" Det.RecSN = Inv.SelfID" and lastly the dates "Det.DDTime, Dep.Start". 

NOTE: Be careful when adding indexes. Specially if you are working in your production database. Do your research first on creating indexes on transactional tables, to avoid locks.

If you already have these indexed, then how many records do you have on each table?

Suggestion: I would Separate the OR conditions in different queries and save into a temporary table, so that I can analyze the data sets and results. Ultimately, querying the temporary tables for the final join.

Rule of thumb: 

query just one record Id, and see the performance.
Always check if index exists.

There may be various issues, and multiple approaches.