I have to work on my laptop with Windows 7's being installed.
Can the possessive gerund be used in this way? In case this phrase doesn't make sense: I'm trying to say that on my laptop Windows 7 is installed.
Using that possessive, your sentence does not make much sense. Windows 7 is the subject in your non-finite clause (the gerund). In your sentence, it seems like "Windows 7's" including the possessive s is the name of the product. That, or the thing that Windows 7 is the possessor of, is missing.
Also, you said you want to express that Windows 7 is already installed on the computer, which means it is no longer in the process of installing it but it has already been installed. If that is your intended meaning, do not use being in your gerund. This makes it progressive and states that the process of installing is still going on and not finished. Instead, use the participle installed.
So, these sentences would be correct:
- I have to work on my laptop with Microsoft's Windows 7 installed.
- I have to work on my laptop with Windows 7 installed.
In the first phrase I shifted the possession to Microsoft who becomes the possessor. You need something it is the possessor of, which is Windows 7. In the second phrase I removed the possessive s. Both sentences mean the same (the only difference is that in the first sentence you explicitly state who is the manufacturer of the operating system).
It is possible to say, but it doesn't mean what you say you want it to mean. If Windows 7 is currently in the process of being installed, then your sentence works. If Windows 7 is already installed (which you say it is), then you would need to say
I have to work on my laptop with Windows 7 installed.
No present participle necessary.