uninstalled play services&google app - system unstable I uninstalled updates for Google App and Google PLay Services apps, and suddenly my phone started to turn off and back on again, non-stop.
I can't do anything because it is up for no more than 10 seconds and then it turns off
I don't know what is the cause of this, since I only uninstalled updates, not whole apps, I'm also not rooted.

I know there are similarly named threads already, but my problem is not with play store not opening, but the whole system not functioning properly

It's Xperia L if I'm not mistaken, and android is jellybean i think

I'd appreciate any help A LOT! :)

Cheers, 
Olek
The phone might still be using the old caches of your old Apps that you have already uninstalled.

So, I suggest you to Go to recovery and try to clean cache and dalvik cache.
Then try to reboot (which may take some more time than usual because you have cleaned all cache) and see it should boot properly.

If this do not help you then you have to go for factory reset as suggested by Firelord.