Well to find out for sure that is the problem (as some sneaky apps and websites say you have downloaded something and then when you click, it actually installs it then, nasty critters) you could try running the tablet in "Safe Mode" and see if the problem persists.
Do not attach it to a computer or risk corrupting the computer as well. Never a good thing.
If, it will let you access "Safe Mode" then you can try and install / run things to remove any unwanted items from the device. If it won't let you access it, in the end, you may have to do a "Hard Reset", which will wipe everything (including your personal stuff) off the tablet. So save that as a last option.
To get into "Safe Mode" please do the following.
1. First turn off the tablet.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe mode: ON" or something similar.
4. If you wanted disable it, simply repeat the steps above, and you should see "Safe Mode: OFF" rather than on.