Ok, driving 10k leds directly from one arduino is a bit of a dream.
My advice would be to separate the whole panel into smaller identical blocks. For example, you can create 8 x 8 led blocks and use 169 such blocks to create your 104 by 104 led display (10816 leds).
To reduce the number of wires, you can use shift registers on each such block to take data in using just two or three wires. If you also add a small microcontroller on each block or a smarter led driver, you could also control brightness of each led.
Keep in mind the power consumption and what leds you're going to use. If your design is going to be in a window or somewhere in the sun, you may have to use more powerful leds to actually see something. You may not get by with 10-20mA leds.
If you connect leds directly to the outputs of a shift register, you have to be careful about the current. A shift register would only be able to handle about 70 mA so if you plan on connecting 8 20mA leds on a shift register, you're going to have problems. You can counteract this by using chips like ULN2803A between the shift register and the leds. Each darlington pair (there's 8 of them in the uln2803a) can handle up to 500mA but you do have to be careful about how hot the chip would get... you can't just connect 8 x 500mA leds to it because the chip is not 100% efficient so it would overheat fast.... but 8 x 100mA leds turning on and off would work fine.
But even with 20mA leds, if you're going to have 10k leds, you're going to have a power draw of 10000 x 0.02A = 200A .. that's A LOT of current. Think how many 5v power supplies you would need to power that panel, and how each of those power supplies will work when leds turn on and off, most power supplies don't like such high fluctuations in power usage.
It would be smart to use small dc-dc converters on each block of leds to convert a higher voltage to the voltage you're going to work with (3.3-5v, depending on led choice and drivers/shift registers/darlington arrays). An 8 x 8 block of 20mA leds would need about 64 x 20mA + about 20mA for shift registers and uln2803a chips so about 1.3A of power when all leds are full on. You can buy dc-dc converters from ebay that use lm2576 or similar chips and convert 12v to 3.3-5v at about 85-90% efficiency and then you could use 2 or 3 cheaper regular computer power supplies to power that huge panel. Less power losses.
Also keep in mind the HEAT generated. If you use 5v and have 3v leds, there's going to be some power wasted in the resistors used to limit the current going into each led.
For example, if you power a 3v led with 20mA from a 5v power supply, then you're going to have a 100 ohm resistor limiting the current which will waste about 40mW of power as heat. Now if you multiply this by 10k, you're going to have 400,000 mW or about 400 watts wasted as heat just in the resistors (not to mention the leds themselves). In time, it adds up... you will heat up the room quite fast.
With 3.3v input and the same led, you're only going to waste about 6mW in a 15 ohm resistor, so 10k leds turned on will waste 60 watts, That's why it would make sense to get the voltage as close as possible to the voltage actually needed by the leds, or use proper led drivers.