Yes, it can appear to be working, while not delivering power steadily, or in ways that are needed, since there are three circuits. Once circuit can burn out while the other two appear to be fine.
It is always wise to replace the power supply when you have other electrical damage.
On the 4700, just be sure the new power supply will have cooling air flow through similar channels to the old power supply... The power switch should be in the same location, and I would avoid a power supply that does not have a power switch... More than half the available power supplys move 4700 air in and out through channels that are partially blocked.
Many power supplies will have extra cables, plugs, and sockets your old one does not. But those differences will usually not harm your computer. You just have to think about some of them and the ways they split apart.
There are 87 different brands that will fit... so consider a name brand with "standard ATX Pr-Ready" like FSP, Sparkle, OCZ, Corsair, Zalman (those five are our choices) ThermalTake, Antec, Enermax Pro, Apevia, Black CoolMax, PC Power & Cooling, Silverstone, Xigmatek, and Antec... provided the power plug, switch, and cooling channels are generally in the same locations.
It is good to take your old one to the store with you or a couple of photographs.
Good luck.