Give it a go, if worse comes to worst, you are buying a new tank.
If silicon is peeling away, or is hard and brittle, then it has perished and needs replacing.
If you push your finger against good silicon, it should be firm but slightly squishy.
Check the silicon between the glass. It should be semi-transparent and have no white or cream patches. It should also be free of air bubbles. If silicon is cream or white, and or has bubbles in it, then the silicon needs replacing.
If the glass is badly scratched, then either dispose of the tank or maybe replace the front panel of glass. Or use the tank as a holding tank.
If the glass is in good shape and has no major scratches, then take it apart and rebuild it.
Use a good quality (brand name) aquarium glass silicon. Make sure it doesn't have mould additives in it. Some glass silicons are used for bathrooms and outdoor windows and have mould inhibitors added. Check the packaging and make sure it says "safe/ suitable for aquariums"
Use a single sided razorblade to remove the glass panel and old silicon. You can go over the glass with acetone as mentioned previously. But then go over it with soapy water and rinse well. Then give it a quick once over with some alcohol. The glass needs to be free of oily substances or the silicon won't bind to it.
The silicon should be about 1mm thick between the sheets of glass. Use tape to hold the glass pains together after you silicon it.
You can buy 90 degree clamps from hardware stores and these sit on top of the corners of the glass and stop them sliding while the silicon dries. You don't need the clamps but they can help keep things lined up nicely. Tape is all we used when building tanks.
Put a decent bead of silicon on the glass where it joins. You want some silicon to squeeze out when the glass is pushed together. You can run your finger up the inside of the corner and spread the silicon out. Then wipe the excess off if there's too much. You can use a single sided razorblade to clean it up after the silicon has dried.
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Silicon should be allowed to dry and cure for 7 days before the aquarium is filled with water. If you live in a cold or humid environment, it can take longer to dry. Follow the directions on the packaging.
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WARNING
Never use silicon in a closed space because the fumes can make you dizzy and pass out. If you are making a tank indoors, try to have good air flow through the room.
If you have to lean over the tank or stick your head in the tank when gluing it, hold your breath before going in.