First thing to do, go to dwarftown, talk to Thrundarr to open the lower levels of the CoC and get your pickaxe repaired. The dwarf smith can only de-rust or repair items in your inventory, not equipped gear, so make sure your pickaxe is not in your tool slot or in a weapon slot when you talk to him.
Begin diving deeper into the CoC. After you pass a certain dying sage, you will eventually reach a level filled with several undead creatures. Be very careful on this level since many of the undead in the centre of the level are very nasty. There are several which drain stats and age (vampires are my least favorite of the bunch). There are also a few liches which will attempt to confuse you so either have a sufficient willpower stat (attainable through morgia root) or possibly some confusion resistance. If you were able to clear the dwarven graveyard with ease, this should not be very difficult but caution is still recommended.
Further past that, you will find a level with water dripping from the ceiling. This will be the first and easiest elemental temple. If you are already reading the guidebook, you will find some useful tips in there but I will tell you now that with your cloak of invisibility, this temple will be simple. However, you will definately need your pickaxe repaired or use one of the wands of digging supplied to you by NPCs, either from Thrundarr if he gave it to you or one you will get from the dying sage.
Finally, while people discourage save scumming as a means of beating the game, it is probably the most useful tool for learning the game. I can garuntee if it weren't for save scumming, I would still be working on my first win due to my many "what if I do this?" strategies. Best of luck to you.
I said it before, and I'll say it again. If I knew scripture like you, I'd prolly be an athiest too.. -gut
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(゚、 。 7
l、 ~ヽ
じしf_, )ノ