This was written after I saw you had resolved the issue (get a new fridge). However, the following tips may help.
Two things to consider:
1) Is the fridge loaded with warm food? If so, it may take a longer period of time to cool everything. I try to pack cool food just before leaving.
Also, is there room for air to circulate? If not, try rearranging stuff. Also, a small, AA-battery powered circulating fan in the compartment might help.
(Is the freezer cold?)
2) Is there an exhaust fan in the external compartment? If not, you might try adding one. I have a
12V computer cooling fan.