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That is the way that its intended to work. Your VPN software will tunnel all network requests to the remote end, and the associated firewall prevents accidental connection between the VPN, and the untrusted local Internet connection.
This is done for security reasons.
Normall when you connect to a VPN, the VPN will completely take over your computer's network connection. This will stop you using the web browser, except to access work intranet, etc.
This is deliberate, because it reduces the security risk of having 2 different active connections where a program on your computer can get privileged access to the work network and also the internet (bypassing your employer's normal internet filtering systems).
Some VPNs offer a setting called "split tunnelling". This does what you want. It connects you to your work, but leaves your internet connection available at the same time. This would need to be enabled your the IT department at work, and if they had any sense, they it is very likely that they would refuse due to the security implications.
Options that you could use to get a similar effect are:
Use a 2nd PC for work, and reserve it for work use for the VPN. Your main home PC will then be unaffected and can use the internet as normal.
Install virtualbox on your PC, and create a new "virtual PC" for work. The VPN connection will be isolated to the "virtual PC" and your main PC will operate as normal. I do this, and it works well. However, setting up a virtual machine is a moderately hard task, and you will also need to buy a new copy of windows to install on the virtual PC.