I'm not an "IT expert," but I know enough to be "dangerous."
Someone else may have some better advice, and if they do, hopefully they will post it, but I think I can hopefully help.
It sounds like you may have some kind of virus...
In short, there is a "real" taskeng.exe which is part of the system. But it sounds like you may have accidentally downloaded a virus that is disguised by the same name. I can't say for certain, but most likely it didn't "replace" the real one, but rather it's just given the same name and likely is saved somewhere else on the computer other than where the "real" one is. It's just named similarly to be more sneaky and less obvious that it is a virus/malware.
See if you can reboot your computer in "safe mode." Here are detailed instructions...
... but essentially, when restarting your computer, just hold down the F8 key. This should allow you to choose to start the computer in safe mode. Hopefully this will let you get to your desktop. It will be a very low-resolution, super-basic version of your desktop. So don't be alarmed when you see that it doesn't look "normal." The goal here is to get you to a point where you can actually do something on your computer.
Once you get to your desktop in safe mode (assuming it works), see if your web browser will work at this point. If it does, download Malwarebytes, which is an anti-malware program. The link is below. There is a paid version with more features, but there is also a free version that you can download. The free version will likely be sufficient for your needs here (that it what I've used in the past to solve issues, including just a couple of weeks ago)...
If you are still not able to use your web browser (and therefore cannot go to the page to download malwarebytes), BUT you ARE able to get to your desktop, and access things like your CD/DVD drive (if you have one) and USB flash drives...
You can go to another computer (perhaps a friend or family member's computer if you don't have another one, yourself) and download the malwarebytes install file. It will simply be an .exe file, so you don't have to actually install the program on the computer that you are using to download it to... you just need to get the file, itself, downloaded. You can then copy that file to a flash drive or burn it to a CD-R/DVD-R.
Once you done this, put that flash drive or disc into your computer that you are having the problem with. Copy the .exe malwarebytes file to your desktop, click it, and install the program. It will have to download updates for the program which will take some time, but luckily you don't need to open a web browser to do so.
Once you have Malwarebytes installed and updated, have it run a full scan of your computer. This may take quite a while depending on the amount of overall files/data on your computer. It will scan everything, and it should pick up on most any "nasties" on your computer. This should hopefully take care of the file causing you a problem, and may even find some others that you aren't aware of and may not be related to this specific problem.
Once the scan finishes, it will list all of the things found, and you can choose to have them removed. Malwarebytes will likely want to restart your computer at this point to remove anything found. Go ahead and do that.
HOPEFULLY once this is done, everything should be back to normal.
Please reply back as to whether this works or not.
At the very least, this shouldn't make anything worse, but I also take no personal responsibility for anything that may go wrong (as unlikely as it is for this process to actually cause any problems that aren't already there). This is simply what I've done in the past when I've had issues with my computer.