I accidentally deleted the network icon from the panel

if you reinstall wicd it should just run

I just uninstaller it with --purge -remove and then installed it again and rebooted and it didn't work.

In any case, wicd is not the problem, I just removed it and don't plan to use it again.

How can I make the network manager icon appear again on the panel?

if you press ALT+F2 and run:

wicd

Does it appear?

By installing wicd, it uninstalls network manager as part of the postinst afaik. I'd just stick with wicd if it's doing the job.

The problem is that wicd wasn't working properly. It couldn't connect and I always had problems with it before, so I just removed it.
The regular network manager seems to be working right now (alt + f2 + wicd says there is no such file) but the icon is not there.

Then i suggest you connect using a wire and install network manager again, you should remove wicd to reduce conflicts.

If you want the try icon for network manager (not required once network manager is configured really but it makes the notify system do stuff). You can press ALT+F2 and run:

nm-applet

To get it back. It's only a config GUI so isn't required to be present to get a connection as the underlying service is configured and running

The network manager seems to be installed and working fine, the only problem is the icon, and nm-applet doesn't bring it back, but as you said it's not really necessary to get online. I'd just want it there in case I ever need to change my network password/settings. I'll guess I'll just keep using the network without it for now. Thanks.

In case anyone else has the same problem:
It was the "notification applet". I had removed that by accident and now the icon is back.