Malwarebytes

You did not get the check box on the second install because on the original install you had it checked, upon uninstallation there are remnants still left in the registry that remembers the previous install.

What you need to do is instead of uninstalling it by the windows remove programs utility, is to uninstall it with an uninstaller such as Revo Uninstaller, after revo uninstalls the program it will search the registry for "leftovers" that the windows remove programs utility never deletes.

Uninstall with Revo Uninstaller > Scan registry with revo to remove registry entries left behind > Reboot > Install Malwarebytes > at the final screen untick enable free trial of Malwarebytes Pro.

You may also want to disable Kaspersky before installing Malwarebytes then re enable Kaspersky after the install is complete. Some antivirus' clash on install of a malware program, especially if they have a malware engine of their own, Bitdefender and Eset are BIG ones, they will not EVEN install if they find Malwarebytes residing on the system.

Another thing to consider .... Kaspersky 2013 is a BIG resource hog, not knowing how much ram you have on your machine, this could be the problem with the crashing you are talking about. If you don't have much ram on installed, I would consider another antivirus or Internet security solution. I have 6 gigs of ram on my Windows 7 tower and Kaspersky 2013 brought my system to a crawl and I don't have a whole bunch of stuff running in the tray or going on in the background, I had to uninstall it and go with Bitdefender.

But what confuses me a bit is because even if you did not untick that box, Malwarebytes ought to revert to the free version after the trial is over

I really do not think it has anything to do with the OS, if you installed windows 7, right click on My Computer , select properties, if you have the Microsoft "Genuine" label down on the bottom right side of the screen that opens up you "should be" good to go, as long as you activated it with the license key which should be located on a Microsoft sticker usually on the bottom of the laptop or for a tower either on the right or left side of it, IF it CAME with windows 7 installed on it originally, if it didn't and you bought this disk on ebay, this guy probably took you for a ride.
With that being said, Even if it's not genuine malwarebytes should still install correctly, has nothing to do with the OS being good or not, if the OS boots and runs, it should install correctly.