Capacitor failures have been mentioned as very likely faults, even on motherboards that are only a couple of years old.
FWIW, there are a number of reasons why present designs of capacitors fail prematurely. The number one reason is stress, whih can result in high ESR equivalent series resistance, or excessive leakage. High ESR and excessive leakage aren't conditions that a typical DMM (even ones with a capacitance range) can test for, either in or out of circuit. A dedicated ESR meter, and/or a capacitor analyzer are required to test for these values.
Forgetting about the counterfeit capacitor electrolyte for a moment (or forever now), SMPS switch mode power supplies and motherbord DC-DC voltage converter circuits apply a lot of stress to today's miniaturized electrolytic capacitors.
Older linear power supplies would typically apply 60 or 120Hz to the filter capacitors.
Newer SMPS apply frequencies of tens of kilohertz, often at high peak currents. These conditions stress the electrolyte and foil coatings in capacitors.
We can see what a similar high frequency stress does to thin aluminum foil when it's placed in an ultrasonic cleaner. Likewise, surface changes take place on lead/acid battery plates when high frequency, high peak currents are applied by desulfator circuits.
Newer, low ESR capacitors are very compact due to the miniaturization of most equipment, and bare space on motherboards is becoming almost non-existent.
Most higher grade capacitors are rated at 105 C degrees to be more tolerant of heat, but poor circuit layout practices often place them where ambient heat is problem. With a nearby heat source and high peak currents, many capacitors are operating close to their breakdown specifications.
It's been mentioned that circuit/motherboards that are shelved when new, may have faults in a couple of years, just from storage. I've seen numerous "new" low ESR capacitors fail testing (badly, not just borderline/questionable), when they're old stock of only a couple of years. That was what started me to test new stock before installing them as repair parts.
It seems that old stock is liquidated to sellers/brokers that package them individually for retail sale and offer them to parts distributors, or just sell them in bulk to surplus sellers. Much of the stock available from the second or third transaction sources would no longer pass new specification testing. They may function in a hobby circuit, but their reliability is likely to be very low.
For important applications, fresh stock should be sourced from a distributor with high volume stock turnover to ensure that the stock has been recently replenished from the manufacturer. There probably isn't any added value in buying a hundred pieces if they'll just sit in a drawer for a year or two.
Many quality electrolytic capacitors have 4 digit date codes on them which are fairly easy to interpret, as week/year or year/week.
One of the best ESR testers by reputation and cost is the Bob Parker/Dick Smith ESR Meter in circuit tester. Other models costing many times more, are no more effective at measuring ESR both in and out of circuit. More costly capacitor and inductor analyzers generally offer more test parameters for more thorough evaluations.
Desoldering thru-hole leads of electrolytic capacitors can be a bit challenging on multi-layer motherboards, but easy enough to do with quality desoldering equipment designed for the task. Random replacement of electrolytics on motherboards may correct or prevent some problems from failed capacitors (and replacement of all the voltage converter and CPU voltage supply capacitors is wise), but I'm convinced that testing capacitors before replacement is a requirement.
Similar to recent comments regarding rechargeable batteries, electrolytic capacitors are also availble in various grades with particular characteristics. The voltage rating and capacitance value shouldn't be the only considerations for important applications requiring any degree of reliability.