Yesterday I had the privilege of losing my Holy Symbol to a story point. (We all lost everything but our clothes.) How can I determine what powers, if any, I can use without my Holy Symbol?
You can use (almost) all of your powers when disarmed and without implements.
When using an Implement (keyword) power you make an unmodified ability check (usually Wisdom-based for Implement Cleric powers) against the target defense (as per definition of attack roll).
When you hold a magical implement (e.g.: a holy symbol), you get to add the implement's enhancement bonus to both attack rolls and damage rolls with Implement powers (and a damage boost in case of critical hit).
Also note that you can take advantage from any implement you are proficient with (not only holy symbols). If your Cleric took the Arcane InitiateDDI feat, then he can use even magical staves, wands and orbs to improve his Cleric powers.
A non-magical implement does not provide any bonus (except for flavor or feat support) unless it is a superior implement. Superior implements cost more but provides a varied array of advantages (properties similar to those of weapons).
For example, the Astral SymbolDDI costs 18 gp but has the Distant (+2 range of ranged and area powers) and Energized (radiant) (+2/+3/+4 damage bonus with Radiant powers) properties. Its base version is non-magical, but it you can buy or create an enchanted version of it.
You gain proficiency with a single type of superior implement by taking the Superior Implement TrainingDDI feat.
Lack of proficiency with an implement you are using means that you gain no advantage from its superior or magical bonus and properties.
When using a Weapon (keyword) power while unarmed, you make an unmodified ability check (usually Strength-based for Weapon Cleric powers) against the target defense (usually AC).
However, unarmed attacks have no proficiency bonus, so you lack a thick +2 or +3 modifier.
When you wield a non-improvised weapon you get a proficiency bonus to attack rolls with Weapon powers.
When you wield a magical weapon, you also get the weapon's enchantment bonus to attack rolls and damage rolls with Weapon powers (and a damage boost in case of critical hit).
Lack of proficiency with a weapon you are wielding means that you don't apply the weapon's proficiency bonus and gain no advantage from its magical bonus and properties.
Some powers may require you to wield specific weapons or implements. In this case, they explicitly state this requirement in their Requirement line of the power block. This is usually found in Rogue powers, for example.