You often have to be wired to the modem to change the IP. If you have a wireless modem and nothing else between you and your internet provider, you might just have to change the IP address of your computer.
The first thing to do is to open a command window and type "ipconfig /all" this should show your wireless link, the IP address of the wireless link, the gateway of the wireless link (usually the modem or router IP address) and any DHCP information.
If you see a DHCP server listed, then you reconnect this way:
ipconfig /release
ping
www.google.com -n10
ipconfig /renew
This should give you a new IP address if you are on DHCP.
If your gateway IP address does not start with "192.168." or with "10.", then you are not on a LAN, but are directly connecting to the internet. In this case, you might not be able to use reconnection at all.
In any case, reread the beginning of Getting Started with Reconnection. You do not need reconnection to use JDownloader efficiently. Just download from multiple hosts.