A PSU from 1999 will be based on the ATX v1.3 standard and will thus have an extremely anemic +12V rail, usually making up 40-60% of the PSU's total rating, rather than the 80-90% expected of modern PSUs. Its effective wattage is essentially halved when powering anything newer than a Pentium 3.
Additionally it will be based on an outdated topology, probably half bridge, single transistor forward, push-pull, or dual transistor flyback. Efficiency will range from 65%-75%, depending on which of these is used and how well it's implemented. Running an Atom system, which will draw around 20-50W (depending on the configuration) may result in even lower efficiency, potentially as low as 50%.
Finally, 12 years is more than enough time for capacitor derating (which is usually an overblown non-issue) to have significant effect on the power supply's capacity.
Basically: get a new PSU.