Hi there!
Sorry to hear about your troubles with your squishy quest! When you have the necessary items in your inventory, this text should appear on the main page of Squishy Quest:
You have the items I am looking for in your inventory! Would you like to give them to me?
Yes, hand in your items!
If you weren't seeing this, it is possible that you might have had a different item than what was asked for (I've totally done this before) or you ran out of time to complete the quest. If neither of these apply, it may be worth submitting a ticket. You can do that from the Rmail screen - there is a Support Tickets link there.
Hope this helps!