How come my computer says it has connection but it has no internet acces?

There might be n number of reasons if there is no internet access.

Firstly check with the hardware you are using for your lan card and LAN card drivers should be updated prior to the vendor. If there are no correct or updated drivers the lan card is incompatible with the OS. It may not work properly.

Second thing make sure you know how to connect to internet by assigning IP address to connect into a LAN. If you are using a router or modem as per their configurations sometimes IP is assigned automatically by DHCP.

If you are using a modem, you need to create a dial up connection according to your internet service provider and a username and password required.

if you are connecting to a switch or router , make sure the lan cable(cat5 cable) is in good condition and use the climper to climp RJ45 clips.

If you are using broadband, some internet service providers may have login page.

If you have correct with all the above details your PC might have infected with virus or trojans etc. 

Before connecting to Internet make sure your PC is loaded with good antivirus system or internet security.