First: Nothing is lost. Yet. It is only hidden from plain view.

Next, the file and menu names below might not be correct. I am doing this from a German OS, and I did not want to reboot just for the filenames.

iPhoto keeps your photos in a subfolder, named "iPhoto Library" of the "Pictures" folder in the user directory. You need to control-click that folder (it actually looks like a file, but it is a folder, trust me!)

Then you will see a popup menu, and the third entry from the top ("show database" or something like that) is what you need. It will open the folder and display its content. One of the subfolders is called "Database", another is called "Masters". The Masters folder contains more subfolders, one each for each year of photos. Inside you will find subfolders for the months and inside again for the days. There you will find all your unchanged photos. If you rotated, cropped or modified them in any way, those photos are in the Database folder. I can only encourage you to explore them and copy all what you want to preserve to an external drive, so it can be added to iPhoto again.

But please fix the cause of the slowness and the crashes first! If your hard drive is dying, make a full copy and work on that to recover your photos.

I'd go for the 'not quite cave-man' approach - though still a bit manual...

• Launch Image Capture.

• Plug in iDevice

• Select any/all photos you wish to delete

• The Delete button is at the bottom of the window [the 'no-entry' sign]

After comments - the button is still there in Yosemite.

Update Nov 2015 - the button is still there in El Capitan, though it is now black & white, not red.

Picture updated to Image Capture 6.7 after further queries on the button not being there.

Update July 2016, as people are still missing this bit...

If the Delete button doesn't appear, eject & re-plug the phone.