For me the solution was quite simple. In game directory find file called dosboxGK.conf, open it with text editor and change line:

cycles=max

to

cycles=fixed 20000

Save file. Start game.
It should help.
Enjoy :)

You wait for Frick to fall asleep
I have to say that the waiting for Frick to fall asleep part is asinine. Getting the beignet vendor to appear in front of the police station should be enough. That said, there's nothing in this game that's as asinine as some of the other Sierra puzzles (King's Quest's puzzles involving Rumplestiltskin, throwing a bridle at a snake, and throwing a pie at a yeti, Space Quest's "Put Gem in Mouth" and "Hold Breath" and Astro-chicken, Police Quest's driving and having to check your car every time or else getting a flat tire, etc.)