While I agree with Torben's answer, the core of this question applies to situations other than just working vs. babysitting.
Sometimes a parent may want to check email, do some shopping, or participate in a wonderful online parenting question and answer community. The issue of a baby wanting to play with technology isn't just limited to computers/laptops/tablets. A smartphone can easily fall into the same category, particularly if, like me, you use it to show your child entertaining and/or educational vidoes, or play music. It becomes much less of a clear-cut issue when it comes down to "how can I answer a phone call without my child demanding to play with the phone?".
While it is still true that the baby needs more attention than you might give to such tasks, including phone calls, there are still situations where it may be very valid to want to use these things in front of a child. For example, when my wife and I are both with my son in the living room, one of us can surf the internet or do work while the other keeps our son entertained, and we prefer to have us all together as a family rather than have one of us have to leave the room.
So, how do you actually handle this without it becoming an issue?
One possible solution is to give your child their own version of the item to play with.
I'm not suggesting you get your child a laptop, or buy them their own iPad. However, there are plenty of toy laptops and cell phones that are age-appropriate. Children love to emulate their parents, which is probably why your son is so intent on playing with your laptop. Giving him his very own laptop will not only channel that energy into something that he can't damage (okay, a 10 month old can probably damage anything up to and including diamond, but at least we're talking a plastic toy that is easy to replace!), it also lets him feel like he's "being just like mommy/daddy".
This can be extended to lots of other items. Toy lawnmowers, ovens and cooking sets, car toys that have steering wheels, etc..
If you don't want to/can't invest in child versions of every item that you don't want him playing with, the only other options I can think of at that age are to either have something else that the child will see as "better" (which can be difficult, given how quickly "favorites" change at that age, coupled with the fact that the item in question is forbidden may only make it even more attractive), or, as Torben suggests, keep anything you don't want him playing with entirely out of sight.