Re:
The printer may connect wirelessly to the router/modem and the signal can travel through the cable to the PC. So seeing the printer doesn't mean that the PC has wireless.
Also, there are a lot of different Inspirion models. Without the exact number, it's hard to find out the specifications.
There is a way to check if there is a wireless adapter in there though.
If your control panel still uses the category view, go to "Control Panel -> Hardware and Sound -> Device Manager (top row)"
If it uses small or large icons, it's "Control Panel -> Device Manager".
Click the small triangle next to "Network Adapters". Your ethernet adapter will be listed there. If there's a wireless adapter built in to the PC, it'll show up there as well.