HP Laserjet P1102W is offline now that I installed ElCapitan

At minimum, you need to reset your printer. Leave it powered and connected to your Mac. Do the following steps. The (2017-10-24) Apple downloadable HP Printer Drivers v5.1 for OS X only provides support for the HP LaserJet Professional P1100, and P1100W. There are no 1102W drivers for El Capitan on the HP site.

Dock : System Preferences : Printers & Scanners panel

1. Right-click your Printers entry for the LJ1102w, and select Reset Printing System…
   1. It will ask you if your sure… click Reset.
   2. You will then be prompted to enter your adminstrative (your login) password
   3. Your LaserJet Professional 1102W Printers entry will be removed
2. At the bottom-left of the Printers window, click the + symbol
   1. An Add panel will appear, and if your printer is networked, its name should already appear in this window.
   2. If so, click your HP LJ1102W name.
      1. This will populate the Name and Use: categories at the bottom of the panel.
         1. Airprint may be the default, so click that selector, and you should see your LJ1102W printer name, so choose that menu item.
         2. Click Add.
            1. The printer options panel will slide down giving you options to select (or not).
         3. Your printer will now reappear in the Printers panel with a green dot that it is online.
            1. Right-click, and make it your default printer.
3. Print something.

If the above does not get your printer working again. Let me know and there may be alternative drivers available.

You might be able to find a driver here.

Gimp - Print

HPIJS for Mac OS X

PrintFab

None of these links has the LaserJet Pro P1102W printer drivers. The HP LaserJet 1100 is a different printer.

The P1102W is a 2010 vintage printer that HP has superceded with the HP LaserJet Pro M102W model for $88. The replacement toner cartridge for this newer printer is $56 (63% of the printer cost).