Here's what I would do:
1. Move the fish into a large rubbermaid bucket (or more than one depending on how many filters you have) along with your filter(s) and heater(s).
2. Drain the water in your tank. You should be able to leave your rocks and such in place, as long as they're not in the way of your repair.
3. Remove the silicone from the corner that is leaking. Make sure the surface is very clean and dry.
4. Re-silicone the corner. Most silicone will take at least 24-48 hours to fully cure (read the directions). Do NOT add water again until it is fully cured. (You can get aquarium silicone from the LFS or you can use any 100% silicone from the hardware store. Just make sure it's not mildew resistant or any such thing.)
5. Add water and wait a day to make sure you have taken care of the leak.
6. Re-add fish. Either do a water change or use an extra heater to make sure you get the temp up to something close to what the fish are in the buckets.
Some things to consider.
Without knowing what fish you have, you'll have to think about whether rubbermaid buckets are going to be big enough for your stock. You'll also want to think about how you're going to cover them. When I was a kid I remember losing half my stock because my tank cracked and I was keeping them in a bowl until I could get to the store the next morning...half of them jumped out. Those egg-crate diffusers for flourescent lights would probably work well. Don't worry about the lights...they'll be fine for a couple of days in the dark. (assuming you don't have any real plants). Feed them very sparingly as you likely will be stressing them enough and you don't want the water to foul while you're doing this.
Let us know how it turns out.
And by the way...Welcome to Aquaria Central.
