Delete key not working in Safari

I am running OS X Yosemite 10.10.4. Thanks for your reply. I will work on it.

Hardware Overview:

Model Name: iMac

Model Identifier: iMac15,1

Processor Name: Intel Core i5

Processor Speed: 3.5 GHz

Number of Processors: 1

Total Number of Cores: 4

L2 Cache (per Core): 256 KB

L3 Cache: 6 MB

Memory: 8 GB

Boot ROM Version: IM151.0207.B03

SMC Version (system): 2.22f16

Serial Number (system): C02NQ6BJFY11

Hardware UUID: 34CECD95-4EF2-5049-B16C-F85273177D91

By the way, I meant to click that your reply helped, but my problem is not solved as indicated. I don't know how that popped up.

I restarted in safe mode and went to Preferences/Extensions. Each extension showed either Installed or Install. I could find no way of turning off an installed extension. There was no uninstall button, nor did that option appear when right-clicking on the extension. Delete key still did not work with Safari in safe mode.

I restarted normally, and the delete key still did not work. However, when I went to Preferences/Extensions in regular mode, all extensions were off - that is, each showed an option to 'Install.' I restarted in safe mode and went to P/E. The extensions previously installed again showed up as installed. I tried the delete key in Safari. It worked in safe mode. I restarted in regular mode, tried the delete key, and it worked.

I am mystified by the whole sequence and wish I had taken screen shots along the way. In any case, my delete key is now working in Safari again. Thank you for your help.

Well, I spoke too soon. The delete key works when deleting in the URL line, but not elsewhere - writing an email in Gmail or filling out a form, etc. So I will go back to my previous remedy - not using Safari and going back to Chrome. (I see that I can delete in writing this reply, so maybe it's Gmail - another battle in the Apple-Google Wars.)

I have been doing without Safari but decided to try adding a new account and testing because I miss several Safari features.

Safari worked fine in the new account. However, when I tried to log out, I could not. Nor could I restart or shut down. It would go to sleep. That's all. I tried force quit and saw that Team Viewer was not responding. I deleted Team Viewer. The computer immediately shut down.

On restarting, the delete key momentarily seemed to work in my account, but then reverted to previous behavior. So, there is something in my user account that is causing the problem. But I have been unable to isolate the issue. Any suggestions? Can I delete my user account and redo? Or do I lose all my settings and data, etc. (Don't really know the correct terms.) Thanks for the create user account suggestion.

Thank you for the reply. I went to the Linc Davis post and followed the instructions - more or less. There were no items in my Library similar to those shown in the post. There is nothing at all related to Safari in the Library or in the Cache. None of the items in Step 3 are shown in my Library (unless I am not in the correct folder. More than one?).

I did uninstall certain extensions and tested Safari in Safe Mode and with extensions turned off. The situation did improve somewhat. The delete key now works when typing in the URL line, and it works when typing an email in G-Mail. However, I still cannot delete any character or highlighted section in any search box. Nor can I use the delete key when filling out an online form. Again, none of these problems occurs when logged in as another user, but I still can't find the conflict within my user account that is causing this.