Usually if you are cleaning it, you are using an alcohol though. Unless you used a watered down alcohol that is. Drying isn't all that important unless that is the case. Now the cleaning head used however can cause damage if it is too thick or in a worse case, breaks off a piece in the console's connector.
Capacitors can fail at any time, sometimes from shorting out, sometimes from poor manufacturing. The signs aren't always obvious but the barrel shaped ones will usually bulge a little from the top or bottom.
That said though, Even Nintendo claims that failure of the connection between the cartridge and the system can cause both flashing screen andscrambled graphics. And my NES's ZIF connector bit the dust back about 21 years ago as well. It had developed a small hairline crack that was hardly noticeable without looking under magnification but would basically render any effort to put a game in useless with Flashing or broken graphics. So Assuming that the system still powers up, try getting a new ZIF connector. It's not like they are that expensive.
I had multiple things associated with the ZIF connector, the blinking screen bit is more in line with the lockout chip failing to communicate between cart and board over the connector. scrambled graphics depends on connection of the other pins involved in the series of pins. Did you ever use something like a Game Genie with your NES? These due to their nature of the design, were pretty stiff and caused damage to the ZIF connector and basically made it so that you had to use it to start your games Even if you didn't want to use it. Best advice, if it's been sitting in storage for a long period of time, it's a good idea to open it up and clean it up from the inside anyway, at least you can get a good look at the connector pins that way,(check for dirt or corosion) as well as check the condition of the caps of the board. (another failure point of these older systems) And while you are in there, do the lock out chip pin snip to stop blinking screen.
If you have the Frontloader NES, the typical failure point is the 72 pin connector that connects the cartridge to the board. It's actually a pretty easy fix with the appropriate screwdrivers, the easily available part, and some time. Then get yourself an Everdrive N8 (pro if you so desire to play massive homebrew titles) and load the games you have to that and never change carts again.
Welp, That's some happy horse shit...