I'm assuming you want help with connections to the touchscreen, not with making your FEZ look like a keyboard to the computer (or with configuring a keyboard as input for the FEZ, depending on your project).
There are essentially two options: Use ADC (analog-to-digital converter) lines on your FEZ to directly connect to the touchscreen, or use a touchscreen controller IC to do the low-level stuff and then connect with SPI or I2C to the controller to get the digital data.
The first option is cheaper (you don't have to buy anything special), but will take more processing time on your FEZ, and will require you to do a little bit of analog design work. Atmel's appnote AVR341 is a good reference, and easily translates to other microcontrollers. Page 7 gives some good requirements: You need a fairly accurate A/D source, 15-25mA source/sink currents, and a processor capable of taking new measurements 70-200 times per second. I'm not sure how well the FEZ works with frequent interrupts like that, so the second option might be more attractive.
The second option eases the processing you'll have to do. Chips like TI's TSC2200 even go as far as to give you a keypad interface so that you can simply wait for the chip to tell you that someone's pressed a key (it's 4x4 keys, not a keyboard!). However, the more features you ask of it, the more complexity will be present in the interface. For a .NET application, you probably want to see an interface rather than connecting right to the hardware,
Regarding the suitability of a touchscreen interface, consider that it can be uncomfortable to type on a rigid surface for a long time, and resistive touchscreens are even worse because you need to apply significant pressure. Don't expect to sustain high typing speeds for very long without causing pain in your fingertips. Also, you'll want some kind of feedback mechanism. The Apple iPod/iPhone/iPad screens are as nice as they are because they (1) indicate the letter you're touching and (2) increase the sensing radius of letters that are likely to come up with predictive algorithms and dictionaries. It's very hard to get a touchscreen keyboard to feel natural.
If the laptop worked you might want to plug it in and plug a logic analyzer or an oscilloscope to the pins of it to snoop what sort of information it's sending.
Even if you can't plug it back in the laptop, if you can figure out the power supply voltage and pins it might start sending data even without an external clock signal.
Here's a link that might be of some use, seems to go into detail - http://www.synaptics.com/sites/default/files/511-000275-01_RevB.pdf
And perhaps this can be applied somehow as well, although seems like the connector has more pins. http://pinoutsguide.com/Inputs/alps_touchpad_pinout.shtml
Best Answer
If you're really after a capacitive touch sensor, this likely won't work at all because the aluminum plate is a short to ground. You're better off making an oscillator (ring or 555 based oscillator's are my favorites) that has a frequency based on R and C where C is two separate contacts where the touch sensor goes. A persons finger near the two contacts greatly changes the dielectric between the two contacts and you end up with a very different capacitance. With a different capacitance, you now have two different frequencies that your oscillator will ring at. It's actually a range of frequencies depending on how close the finger is, but that will be turned digital at the end.
Then you send the oscillator output into a high pass filter (small capacitor in series), set the DC operating point and then use a comparator with a chosen voltage level to determine whether the person's finger touched it or not.
There's always digital versions if you wanted to travel into uController land. Here's an app note by TI on capacitive touch sensors. A lot of the front-end concepts are the same regardless of whether you want to go digital immediately or just keep it analog until the end as I described above.
simulate this circuit – Schematic created using CircuitLab