Hi!
It's A500 boot problems today!
(just because I posted on a similar thread)
Well, it's difficult to say precisely, but despite not excluding a capacitor problem (but rare on non-SMD machine IMHO - never heard of it), I think it's something related to the motherboard and solderings nearby, since the leaking acid.
They may appear good, but they simply don't connect properly.
The fact that it works after some on-off switching, it's a sign of this problem in my experience.
Solderings are not very bad, but at the beginning they don't conduct properly: they need to be "stressed" by some voltage on them to start "working".
It may sound strage, but it happened to me in the past on other equipment (or they provide just an intermittent contact).
In my personal experience I had an A500+ from a friend of mine suffering of not booting problem with power LED blinking, and all of that was due to battery liquid leaking.
It ruined many solderings and contacts nearby, and I needed to make a few bridges around chips on the datapath (74LSXXX): solderings appeared ok, and PCB tracks too, but no real contacts (I had to check with a multimeter).
Everything solved, and I placed a button battery (CR2032) in it.
Hope you manage to solve (but you need some basics of electronics).
C U!