Power converter that worked in Barcelona doesn't work in Rome – how to recover?

Pardon me if this was said and I missed it. There is probably a lamp, and maybe a coffee maker, hair dryer, or iron. Does it/they work in the same socket? Have you tried more than one socket?

These two things should be checked along with the adapter and chargers others have mentioned.

I think the part of the question about the adapter working in Spain and not in Italy is of general interest to maybe some other people thinking to travel to Europe and questioning themselves about adapter, so here it goes

If, and I repeat if, your adapter is like the one in the photo, then
I’d say that you are lucky that it worked in Spain without frying your phone charger.

USA use 110 volts.
Spain and Italy use 220 volts.

Your adapter is just a pin adapter. I quote from the description of the one you linked, and if your is more or like the same be assured that this apply to you too:

This universal plug adapter is not a power converter,it just converts
the power outlet plug type only, it does NOT convert electrical output
current and voltage. Please make sure your device carries a
electrical converter when you travel to other countries with different
electrical output.

The voltage and current ratings printed on the adapter is just to tell you in which condition it is safe to use it, not that it somehow understands itself which combination of input and output voltage and current the connected device need.

So, to make it short and stay on Travel.se topic:

• Your adapter is probably just a pin adapter
• Maybe in Spain you found a better power line or maybe the opposite, and that made your charger work
  _{220 volts is the theorical output. Italian power lines can go from 200 to 240 volts, sometimes even from 190 to 250, and who knows in Spain}
• Maybe you were just lucky to not have fried everything (yourself included; be more careful next time, please!)
• When traveling you need both a pin adapter and a voltage adapter

Finally, the simple solution (OT per Travel.se, but who cares): if there is a TV in the room that you can disconnect from the power plug, disconnect it and reconnect with your adapter in between. If the TV works, your adapter is ok and everything I wrote above is correct. Or, even easier and less dangerous, ask at the desk if they can try the adapter with some appliance they have. Surely one of them will have a phone charger to try it.

Although European countries have different plug & socket standards, they are mostly compatible as long as you can fit one into the other (e.g. you may be unable to use a German plug in a French socket). Also, the light on your adapter comes on, and the phone charger works, so the socket in your hotel room looks fine.

The only reasonable explanation I have is that your plug adapter broke down, since it’s near impossible that your charger AND your tablet power supply both broke at the same time. You should buy a new adapter then.

The item you linked to has a surge protector built in. Have checked to see if yours tripped the surge protector?

If you tripped the circuit breaker or blew the fuse, then no power would reach your charger.

The adapter linked to in your question is not a power converter. That is a plug adapter which changes the shape of the connection but not the voltage or frequency.

As long as the device you are plugging into it is also voltage-switching, it should work. If it does not, then the adapter either died or the hotel outlets are not functioning properly. Unfortunately, if they are not, then it may be the cause of death of the adapter.

Now, if your device is not voltage-switching, the power in Europe which is higher than that in the US, will most likely fry your device. So be sure to read the compliance of every device and charger you connect.

To replace your adapter look for:

• The same type of plug converter if your devices are voltage-switching. Those are usually called Universal plug adapters. You can also buy one which is specific to convert US-to-Europe plugs which are much cheaper and smaller.
• An actual power converter if they are not. Note that power converters have a maximum wattage, so be sure to buy one which can support the devices you intend to plug.

There may be something wrong with the adapter, or it may be something else. You can try and isolate the problem. The problem is either:

A: The electric sockets in the hotel room.
(This seems unlikely since the European USB charger works.)

or

B: Your plug-adapter. (This is what I’d personally bet on.) BTW, Italy has these funny three-pin plugs, maybe that’s related? (Thanks, @shoover.) Or maybe it just recently broke in in some way?

or

C: Your devices. (There are two of them, so this seems less likely. That is, assuming they do support up to 240V.)

1. Try the European USB charger in the plug-adapter. (Thanks @user568458.) If this doesn’t work, then you know it’s B and you can skip straight to 3. If it does work, then move on to 2.
2. Take your tablet and battery charger to a coffee shop or library or something like that and try to charge there, to see if that works. If it does, then it suggests A. That would mean you could complain to the hotel. If charging doesn’t work in the coffee shop either, then move on:
3. Go look for a new adapter. Rather than telling you what to look for I’ll just advise you to find a shop that lets you try (with your own devices) before you buy. That way, you’ll know for sure whether it works or not. It’s also good if there’s a shopkeeper who can assist you. Ask specifically about the three-pin thing. If someone assists you, and even new adapters don’t work, then it suggests C. (Which is another story.)
4. If the new adapter does work in the shop, but still not in the hotel room, it suggests A. You can then consider asking for another room or to have it fixed.

If, after returning with a new adapter and it then works in the hotel room, it suggests B.

Here’s the same advice expressed in a diagram: