If you have successfully configured your DIR-825 to forward the port, you should try remote viewing from a different location. Assuming your router is set right, the problem could be with the connection on the remote end.
Robbr brought up some good points. It wouldn't hurt to double check that your router is forwarding port 5001 to the right IP for your Slingbox.
Also, go to support.slingbox.com and log in. You should see information about your Slingbox, make sure that it says Setup Complete: Yes under Internet Viewing. If it doesn't- and especially if you get any alert notices- you likely haven't quite got the router configured.
Since I'm at college, I can't work on my slingbox error until I get home on Wednesday. But I'm not sure what it is because when i go to slingbox.com, i can watch my TV, but when I go online from the slingplayer, it will not work. An alert even comes up when I check the status, despite me being able to watch from the website only. I thought it might be my Kaspersky firewall, so I set an exception for the port and the slingplayer itself. Any other suggestions for what might be the problem with being able to watch on the website but not via the slingplayer?
But I'm not sure what it is because when i go to slingbox.com, i can watch my TV, but when I go online from the slingplayer, it will not work. An alert even comes up when I check the status, despite me being able to watch from the website only.
Okay, it's coming together now. There's something wrong with the way port forwarding is set up at home, that's why you're getting the alert when you check the info box at support.slingbox.com. It's also helps explain why the Web Player works but the full SlingPlayer app doesn't.
When you set up port forwarding, you're sending incoming TCP traffic on port 5001 through the router's firewall and on to the Slingbox. This is the normal way Slingboxes handle remote viewing, and it only works if everything is configured properly.
Newer Slingboxes and some Player versions can also get through using the UDP protocol instead of TCP. UDP helps because it doesn't rely on port forwarding, but it doesn't work in all situations. That's why the Web Player is getting through for you, it's switching over to UDP.
SlingPlayer app prefers TCP. While it can use UDP, it doesn't switch protocols gracefully. Right now it isn't working because it's stuck trying to get through on TCP and it fails when it gets to your router.
You can get more information including how to reconfigure SlingPlayer for UDP here. (placeshiftingenthusiasts.com)
I'd suggest leaving things alone for now. You mentioned that you'll be returning home soon... I think trying to force SlingPlayer to use UDP is more trouble than it's worth since you'll be able to fix things properly in a few days. I say stick with the Web Player until you get home and fix the router settings.
When you're home, go in the router config and check this:
Click to Enlarge
Pay special attention to the Protocol dropbox under Traffic Type and the IP Address. The IP address is what your Slingbox is assigned on your home network, and it should match the Slingbox Private IP Address listed in the info block at support.slingbox.com.
Note that once you connect your computer back up to the home network, you'll be viewing Slingbox locally. SlingPlayer should start working instantly since port forwarding isn't required for viewing over the LAN. Don't let that confuse you- you still need to get your router sorted out in order to watch away from home over the internet.
Give that a shot. Post back and say how it goes.
Good luck !