|You don't have a network slot, you have a wired network port, like a larger telephone cable port.|
If the computer is running, an led will often light up at the network port when you merely have a working network cable connection between that port and whatever port is at the other end of the cable, such as a port in a router, high speed modem, or a combo router / high speed modem.
That led, or another led beside it, will blink when data is being transfered through the network adapter.
The network cable (all network cable connections) must be okay . The cable sheath surrounding the wires at either end should be under the clamp in the clear connector on both ends of the cable, and the end connectors should "latch" into their ports so that they are not loose - the plastic lever on the end connectors should not be broken off, and the cables should not pull out of their ports when you gently pull on them, they should only pull out when the plastic lever is depressed.
If the drivers for the network adapter connected to that port are installed properly, you will see that network adapter listed as working properly (in Device Manager) or shown in certain places in Windows (My Network Places - Network Connections). That indicates the network adapter is working, and in My Network Places - Network Connections, that you have a network connection to something ( if there is no red X there) - a router, high speed modem, or a combo router / high speed modem - but not necessarily the internet,.unless there is an Internet Connection icon there that says it's Connected.
If you have a DSL or an ADSL high speed modem, or a combo router / DSL or ADSL high speed modem, you're more likely to lose your internet connection more often for several reasons.