Cannot create folders/alias on desktop

Hello, Kitty! ...And welcome to Apple Discussions! 🙂

You may have to restart the computer with the Shift key held down so as
to have it start in SafeBoot mode. This would show a login box and then
after awhile, the desktop would appear. However, this is not the end all
and the next suggestion while in SafeBoot would be to find and run the
computer's Disk Utility, in the Utilities folder. See "GO" in the Finder menu
header and click that name, to see a drop-down menu of items; choose
Utilities Folder there. In that folder, when opened, find/launch Disk Utility.

In Disk Utility, be sure to click on the name in the left side margin, of
the computer's hard disk drive. The default name is often Macintosh HD.
Then choose 'repair disk permissions' and when it is done, you could
quit Disk Utility and restart the computer normally.

If that does not help, then you may have to start the computer from its
OS X install-restore (or most recent boot install DVD) by holding the C
key down while the computer has the DVD inside its optical drive; and
then when the Installer appears on the screen, there should be a menu
in the header or top of the screen (like in Finder, it would say Installer)
and you should be able to choose from items in a Utilities header, to
launch Disk Utility from within Installer's menu bar drop-down choice.

With the booted version of Disk Utility in the install DVD running the Mac
you can choose to 'repair disk' and also 'repair disk permissions' and it
may also be good to choose the brand name of the physical hard drive
in the left margin of Disk Utility and note you can Verify the hard drive;
note if the SMART status indicates if the drive Passed.

If the Disk Utility indicates, when using 'repair disk' that an error is noticed
by the utility, be sure to run the utility again and see that the drive is fixed.
If for some reason the disk utility can't repair disk, note the message and
refer to it later if the computer should not respond correctly to this effort.

(Be sure to not actually begin the Installer, since at this point, the idea is to
use the Disk Utility within it, and not re-install the system in your Mac.)

Also, if your computer's main user account (admin) and/or computer's
short name has been changed incorrectly, the user may no longer have
permissions or privileges to do many normal things in the computer.
Some things have a specific way to do them; and if they are done other
wise, stuff can happen.

Since I am only speculating after a point in time, I am hopeful your Mac
can be up and running with a few actions and then later, maintenance.

There may be some other reason for the computer to be acting improperly
so this is a matter of 'trial and error' troubleshooting; and it may take time.

Good luck & happy computing! 🙂

{PS: I always wanted to say 'Hello Kitty' to someone other than a kitty cat!}

For some degree of preventative or routine maintenance, you could
get and try a free-running utility interface tool (as I call it) by the name
of OnyX from Titanium Software. The version for your OS X is among
other versions (different systems have their own) and the tool does a
few things, most casual users may not know, can or should be done at
some point in time or another.

• Titanium Software - OnyX (choose version)
http://www.titanium.free.fr/pgs/english/apps.html

With this in my Macs, I use it occasionally; usually when I intend on
restarting it anyway (mine is asleep when not running, for over a
month at a time; and it also has an uninterruptible power supply so
it will not get surges of high or low power from the grid) and have
this OnyX set to run in its Automation mode, and since I don't care
if it clears caches, I have it run all check-box items. Also, it can be
set within its own preferences to restart automatically when done.

There are a few other similar products out there, but for general
use every so often (maybe once a month, depending on runtime
of the computer and what you do with it) it helps.

Also, when installing software or updating the OS, be sure to run
the Disk Utility's 'repair disk permissions' before & after the install.
This somehow helps the OS X and the apps to work better.

Thought I'd add these bits of information since I did mention in my
first post there were other things one could do for preventative help.

+Best wishes & regards from Alaska!+
Good luck & happy computing! 🙂