A solution after researching issues with scanning and receiving the above errors when attempting to scan over a wireless network.

1. Identify the IP address assigned to your 3310 All-in-One, by pressing Setup -> 7. Network -> 1. View Network Settings -> 1. Print Network Configuration Page on the 3310 printer. The section you are looking for is 802.11 Wireless (or 802.3 Wired, if you are connecting with a network cable). Within the section, locate the line IP Address. Make a note of this number

2. Open the file C:\Windows\System32\drivers\etc\hosts using Notepad. You should see two entries (there may be more, depending on your PC setup):
127.0.0.1 localhost
HP7A4A24.Belkin HP0017A47A4A24

The HP entry is the important one (yours will have different numbers and letters after the HP letters, and may a different ending, depending on your wireless router). Add two entries before this line, where 192.168.2.3 is the IP address you obtained in step 1, and the two HP text strings are already in your HOSTS file:
192.168.2.3 hp7a4a24.belkin
192.168.2.3 HP0017A47A4A24

(Incidentally, the local domain suffix ‘belkin’ appears to have come from the Wireless router – despite not setting a local domain suffix on the router! This meant when a lookup on hp7a4a24.belkin was performed, it could not resolve to an IP address (i.e. 192.168.2.3), therefore scanning functionality would fail).

3. Download and run the HP communications fix from http://h10025.www1.hp.com/ewfrf/wc/genericSoftwareDownloadIndex?cc=us&dlc=en&lc=en&softwareitem=sj-32245-2&jumpid=reg_R1002_USEN

4. Right click the “HP Digital Imaging Monitor” icon in the taskbar (if it’s not running, you’ll need to run it).
- Click “Launch / Show HP Solution Centre”
- Click Settings -> Scan Settings -> Scan to… Setup
- You can choose the Scan Destinations; these are the options that will appear on the printer when you press the Scan button, and allow you to determine where the scanned image is sent to (for example, a program such as Microsoft Word or Paint, or alternatively to an image file, which you can then view and edit using your own software as you wish)
- Choose “Save to File” by clicking on it, clicking on the Right “add” arrow, and then click OK

5. Test the Scanning functionality
- Press Scan on the printer
- Press OK when 1. Select Computer is selected
- Press OK when you select your computer from the list
- Press OK when you select the “Scan To” option (in our example, we should only have “Save to file” available
- HP Scanning software splash screen should appear on screen and run, the printer will scan and save the file to your PC
- Printer will confirm scan completed by displaying “Scan was sent. See computer monitor for results.”
- PC will confirm scan was completed by asking if you want to Scan another picture, or click Done to finish.
- Windows Explorer should open a window showing the scanned image