Question: I just restored a SP 2013 Foundation site collection into another farm.
The restore seems ok, but the web front end of the main site is totally missing CSS. 

The subsites are OK: they all are using the standard 2013 layout with different colours.
I performed the backup and restore by `backup-spsite` and `restore-spsite` respectively.

Answer: 
Did you change any modifications on front end style loading? like manipulations in .

May be previous site is loading because of that resource is cached in the browser. Just clear the cache and check on old machine, if it also not working then my clue is correct.
The ultimate solution was in the database size. We were restoring on a MSSQL express a database whose size was beyond the size supported by the Express edition.
We smoothly restored on a MSSQL Standard Edition