I tried to paint my downstairs bathroom vanity last Tuesday. The cabinet looks like dark oak but it is actually just a shiny plastic sticker laminated over cheap particle board. I lightly sanded the doors and brushed on a standard water based primer. It went on smooth and looked completely fine until it dried.
I accidentally bumped one of the doors with my vacuum cleaner the next morning. A huge chunk of the white primer peeled right off the fake wood like a sunburn. I scraped the rest of it off with my thumbnail in about three minutes.
I ended up having to wash the doors with a heavy degreaser and buy a specialty bonding primer. It is oil based and smells absolutely terrible. I had to open the tiny bathroom window and leave the exhaust fan running for six straight hours.
It actually worked. The heavy primer stuck to the slick plastic perfectly. The cabinet paint on top of it feels like a hard protective shell now. If you are trying to paint fake builder grade wood, do not use the standard wall primer you already have in the garage. Buy the heavy oil based can and keep the doors open.