If it cranked with a boost, and kept running when the cables were removed, you most likely have a bad battery.
The whining could
be the Alternator working hard, trying to make something of the bogus Battery. The same could apply to when you asked it to work hard by turning on the A/C Fan etc. Althought that system can cause it's own whine as well....
You would do well to have both checked. The bad battery could well have damaged the alternator electrically.
I'd also check the trunk for your mother-in-law, they whine often and with the fold down seat they can get pretty loud