Hello,
if properly soldered 15 years ago, your complete electronic circuit is much more durable compared to the storage of the single components.
(I have many measurements instruments here, which are 10, 20, even 40 years old and still working very well)
That especially goes for the solder joints which may oxidize on their surface only, which would prevent a good soldering to-day, but in a soldered state, the bulk of the joint is obviously ok, and that counts.
These solder junctions on "stiff" SMD packages may deteriorate only by strong temperature shock of -40/+60°C, > 500 cycles , (as in a car over the years) , but definitely not by storage in a basement of a house.
Also, vibration of several g or bending of the PCB or so might crack the solder joints, or the components themselves.
There are some classes of electronic components, passive components, which do not withstand storage so long, especially when the circuitry is left unpowered.
All semiconductors normally survive a very long time.
These sensitive components are especially wet electrolytic capacitors, which either dry out, or their "forming" decreases. That is their inner Al2O3 dielectric film on the Al electrodes.
If you power your circuitry up, they draw a lot of current, due to the re-forming process, and then may blow up, or may damage the surrounding circuitry.
Old circuits have to be powered up very slowly!
(How did you do it, after 15 years??)
Tantalums are not prone to that effect, because they are "dry" electrolytics.
But those old ones may be produced badly, and in the circuitry charging current limiting may not have been foreseen, so they also may burn.
If you want to replace them by other technologies, you have to pay attention concerning low ESR value, if they sit around linear stabilizers, otherwise latter one may start oscillating.
From what you describe, that you stored the electronics in a closed (taped) box, you may have enclosed a lot of humidity inside the box.
Especially paper attracts humidity from the environment and creates a fine humid atmosphere around the PCB.
Don't you believe that? Those paper packing cases which are left in the basement, begin to smell heavily after a few months already, guess why.
If you have left dehumidifiers in the basement all the time, the whole room very obviously has problems with high humidity..
You did not add a hygroscopic salt bag inside the box?
Well, then several of your components definitely suffer from rust , which probably can be seen under a microscope:
If you initially used cheap components, the protective coating may have had microscopic pin holes, where the humidity entered and destroyed the resistive layer. Especially thin film technology is sensitive to that effect. carbon resistor maybe also effected , but you can easily replace these by the much better thin film technology, if you also have through hole components on your PCB.
Then, if you used solder with a lot of flux, and did not properly remove that, and did not protect by plastic spray or so, this flux may have aggregated humidity even at lower level of air humidity, and then a chemical process using salts may have destroyed the solder joints, or the PCB traces.
Another effect are whiskers, if you used bad solder alloys. They may cause shorts, and are barely visible.
Also, you may have introduced ESD failures 15 years ago, which now show up.
High resolution, sharp, macro photos of your PCB would help.
(I'm working in the development of an automotive electronics supplier, being sort of a component technology expert, and may tell a lot about long term storage and component failures)
Frank