Broken non-standard laptop parts
Monitor, monitor hinge, chasis, motherboard, etc.
Unfortunately replacing broken non-standard laptop parts (besides the hard drive or power adapter) is very often an expensive repair that requires dismantling the laptop apart (total labor rate of $120.00).
Please note that Palisades Computer Repair does not perform monitor "repair" or "refurbishing" -- only replacement of the entire assembly. Some specialized repair shops may or may not be able to repair a damaged monitor without buying an entire monitor assembly.
Additionally non-standard parts are typically only sold by special order and at a premium by 3rd party vendors. So if your laptop is 3 or 4 years old then it is very often NOT a cost effective repair.
If you DO wish to proceed with the repair, often the cheapest solution is to wait and buy the same exact model computer off of Ebay, then "cannibalize" it for parts. Often broken laptops, or even laptop "shells" (with missing parts) are sold on Ebay for cheap (perhaps $25 plus shipping).
YOUR QUESTION: The power adapter connector on the side of my laptop has broken loose on the inside of my computer. Would this require ordering of expensive non-standard parts as well? No. Usually these parts are about $3.25. PCR's labor rate is still $120.00 for this repair.