I am trying to access my home computer remotely (through http). I did a quick test yesterday, and it was fine. But today, I started the VPN on it this morning, it is sending all traffic through it. And now I cannot access it (request times out). Is this because of the VPN? I kind of see why it could happen, but also why it maybe should not. I'm just not sure.
I'm not 100% sure I understand your question properly, but I'll give it a shot.
Here's what I think I'm reading in the question:
If this is an accurate description of the scenario, then your hypothesis is correct - the VPN tunnel is blocking you from accessing your home computer.
The reason this occurs is essentially because the "P" in "VPN" stands for "Private". That means that, once the tunnel is established, the computer or network on one end will only be able to communicate through the computer or network on the other.
To put it another way: If your home computer is connecting over VPN to your work network, the end result is almost exactly (with some variables dependent upon your company's network topology and configuration) as if you'd taken the computer into your office and plugged it into a network port at your desk.
While the tunnel is established, your home computer will only be able to access resources available on your company's network. If your company permits its networked devices to connect to the Internet, your home computer will (usually) also have Internet access while VPN'd to your work network. However, it will likely also be subject to the same Firewall and Proxy restrictions put in place on your company's network.
As long as the VPN is established, you will not likely be able to connect to your home computer from any computer that is not on your company's network. You probably won't even be able to use your home computer to access shared drives and printers on your home LAN, or allow other computers on your home LAN to access the VPN'd computer. Additionally, computers on the Internet at large will not be able to connect to your home computer. Also, it is likely that Firewall/Proxy restrictions will not permit computers from your company's network to connect to your home computer even if they know the IP address assigned to the VPN tunnel.
It is possible, with the right configuration. Maybe the VPN is somehow misconfigured to send all replies back through itself, which wouldn't work. Or maybe the VPN changes the firewall connection while connected, as iszi suggested.