No. It stopped working not it never worked, therefore 12V, 5A must have been enough to run it originally unless the nameplate rating is a pure lie. Figure 0.3A for the fan, and the Peltier modules must either be 6V <4.7A. or thereabouts, in series or 12V <2.35A in parallel. Repeatedly thermally cycled Pelter modules tend to go high resistance so the best bet is to test them individually on your bench supply and see what current they draw, and how much temperature differential they maintain, while letting the old PSU power the fan. If you don't have a bench supply, 12V from a PC power supply or a car battery (not running), with a 10A fuse in series for safety will do to test them, individually if originally wired in parallel and together in series if originally wired that way. If they are in series, note the midpoint voltage. If they draw very different currents, or one is far less effective, or for a series pair if the midpoint voltage is far from 6V, you've got at least one bad module.
Once you've found out out if they are OK and how much current they actually draw, you can spec a power supply, on the basis that one from a recognizable 1st world brand manufacturer will probably survive running at 80% of its nominal rating (even if its actually made for them in China) but an off-brand 'Chinesium' one is unlikely to last running over 60%. Derate both further if its got to run 24/7 or in a hot environment.
If the Peltier Elements aren't OK you'll probably need to replace the pair, preferably with ones you can find a datasheet for. Caution: if the new modules are more powerful it may ice up on the cold side. This is self-perpetuating as the ice blocks the air flow and significantly insulates the cold plate. If your unit has a thermistor or other temperature sensor in contact with the cold plate it may already have an anti-icing circuit. If not, you'll need to add one - a temperature sensing relay board set to activate just above freezing will do the job, wired to cut power to the elements, so residual heat on the hot side can warm the cold side enough to melt any ice that's starting to form. It should be set for a fairly wide hysteresis range (at least 5 deg C) so it doesn't short-cycle which would be very hard on the elements.
I'd also want to replace the cooked fan . . .
It *MAY* be cheaper to simply get another complete dehumidifier as good PSUs aren't cheap, then either keep this one for spares or until you can scrounge up the parts cheap to fix it as a backup unit.