They are right, you probably didn't lose connection to the GPU because of the water damage, but shorted something out. Reflowing things is likely to break more things than it might fix.
If the computer hasn't been stripped down and cleaned, that would be about as much as I would do to attempt a fix without some serious electronics knowledge and diagnostic tools. Even then, not really worth it for an inexpensive model. Time and labor on such an endeavor would cost more than the computer.