1996 Chevy Blazer starting

My blazer wont start sometimes. This time I tried for half an hour so I left it. I changed the fuel filter, which helped for a couple weeks. I gave new sparkplugs, bleed transmission and brake fluid, took out an alarm that had cut of the engine until I removed it. When I turn the key to on, I can hear humming under the car and a fast quiet clicking behind the dash/under the hood by the carborator.(I hope its called the carborator)both the humming and the ticking only last for about 5 seconds or so. About as long as the long beep that every car makes when the key is in first put in the ignition. The battery is brand new, I have all my lights and power. The engine and the car runs fines when I do get it started and drive it. There is no other noise when I turn the key to start it. Ohh! Sometimes if I hold the key down/forward, it"ll suddenly start. After10 seconds or so of holding it there when trying to turn it over. I dont do it often though. Please help.I need to at least get it started to take it to trade it in tomorrw. Please and thank you