It's not unusual for those switch mode power supplies to fail like that.
(A tip when trying to open a sealed mains adaptor, place it in a vice and squeeze it along the seam where the two halves of the plastic case are stuck together. It should crack open. After repairing it, superglue it back together again. I've repaired quite a lot of them, even though they are designed to be throwaway items.)
Bear in mind that if the power supply has been running for 2 years continuously, it will have accumulated more than 10,000 hours use. That could be the rated life of those capacitors in that situation. Switch mode power supplies are quite tough on electrolytic capacitors. There are pulses of high current, often thousands of times a second. The high current pulses can cause the capacitors to get hot, which decreases their life, and eventually they burst. Ideally, suitable low ESR capacitors should be chosen for switch mode power supplies, but as always, companies are tempted to cut costs and use the cheapest components. Also, the manufacturer of your digital photo frame may not have made the power supply to go with it. They probably bought it as a ready-made unit from another supplier, and again, probably the cheapest supplier. Even big-name companies like Apple have been caught out by buying power supplies and capacitors from cheap, low-quality sources. Just because you buy an expensive branded name product doesn't guarantee it will last longer.
On the plus side, I've been able to get hold of lots of newish broken electronic stuff very cheap or free, and fix it easily by replacing the burst capacitors. The same faulty switch mode power supplies are found inside almost all modern electronics like DVD players, digital TV set top boxes, DAB radios, LCD TVs and monitors. I used to get these from car boot sales (and from the dump before they stopped the public from buying electrical items), fix them and use them myself or sell them for a bit of extra money.