MTF, good to hear you are doing better.
There's a few thing you can have with some help from Robie and the nursing staff to make things a bit easier for typing.
Assuming your supine position cannot be changed due to medical reasons, here's a couple of recommendations:
Have the nursing staff find an overbed table that can tilt. Have someone find a way to attach the keyboard base of the laptop to the table while tilted so the screen can be seen and the keyboard more visible to you. Multiple long velcro straps (12-18 inch long - think commercial electrical section or hardware, Home Depot) strung together have worked for me in the past as they are adjustable, strong, and thin. Alternatively, use a flat overbed table and get a foam or sponge wedge with a lip at the bottom to prevent movement.
Be sure to have the power supply plugged in, and the laptop's cooling vents unobscured to prevent overheating. That should help a lot to provide better visual and tactile access for you.
Another option is to get a wired or wireless optical wheeled mouse with a sturdy flat mousepad mounted on a relatively small hard flat surface that you could have in bed at your side (a thin piece of masonite, plywood or similar with mousepad glued on). This will allow you to click and scroll without having to use the keyboard for navigation. Going to the control panel and adjusting the mouse parameters will allow more movement with less motion of the mouse if you prefer. The mouse reduces arm, wrist and finger movement while allowing for computer use - helps to reduce fatigue from trying to move in awkward positions.
To type with the mouse, go to Start, All Programs, Accessories, Accesibility. You'll have a menu which can provide options to configure Windows to help you use the computer. There should be an option to use an onscreen keyboard which can stay "on top" of your window. You can then use your mouse to peck/type in Word, dialog and reply boxes, and for web addresses. There are a few options for the keyboard so be sure to explore its menu settings. For example you can set the keyboard to type when clicked or just hover over a key for 0.5 to 1.0 seconds.
You can also use the Accessibility wizard to set up larger fonts, keyboard shortcuts, click sounds, and others.
There's also a magnifier to make selected boxes or texts easier to read. There's also a narrator program that can read text to you.
Be sure to set up your browser to have bookmarked pages as one click links on a bookmark bar to reduce repetitive typing. Of course, AK should be the first one!
Hopefully these things can help you get better functionality out of your laptop till as your condition allows. Hope this helps!
Bart