Kaspersky has a historical record of not doing clean uninstall. The Sony support guys probably know that too, but since the support calls are recorded, that won't tell you about that in phone calls. This is due to the fact that most antivirus are not updated by Windows Installer, so if a major update is happening in between, the code for current application components and the uninstaller won't match. And this is especially bad for Kaspersky because many of their components rooted deep in system level.
My advice for these kind of "preloaded trial antivirus" software is that, either you decide to run through the trial period and upgrade it to paid version, or just uninstall it on the first time you turn the PC on so the uninstall can happen before any major update is applied. This will save you a lot of pain later.
If you've not done full system recovery yet, you may try your luck to contact them (need to try your luck because you're using trial version, not a paid one.).
Anyway I always (note that not "almost always", just "always") wipe the drive clean and reinstall Windows from scratch whenever I need to buy branded PC. Others here also do that not for no reason.
Really? That's very interesting, about Kaspersky having a poor uninstall record. I suppose that Sony puts Kaspersky onto their new systems and most users just stay with whatever came with the system.