pump will only prime when basket it out

[AndyT86]

If the basket was preventing the lid from sealing, wouldn't I have seen the shaving cream being sucked in?
There would have been some indication that it was sucking air right?

That's right. You can prove this to yourself by closing a piece of straw or something thin across the seal. The tiny gap it causes will be sufficient to make the shaving cream suck into the hole.

Perhaps the basket has that effect on the efficiency of the pump. You said that with the basket you are not getting the same pressure you used to. I forget... Is the pressure different with the basket than without the basket?