Suggest that you invest in a obdII code reader. If you already have one, disregard my suggestion. It will help with your diagnosis of problems, and is relatively inexpensive. I purchased mine on Amazon for around $35 US dollars. I've seen them on Ebay for around $15 and up.
Good luck with your diagnosis.
2006 GT, Strut Tower Brace, Gas Hood Struts, FR Intake Plenum cover, Metal Fuse Box cover, Moroso brake reservoir cover, Rear shock tower brace, Front Bumper Lip Spoiler, JVC DVD Head unit w/ back-up camera, satellite Radio and USB input, 2 - 12" sub-woofers, 4 - 6"x8" speakers, 2 - 6.5" speakers to replace the door subs, 3 amplifiers, LED lights under the hood and in the trunk, chrome e-handle on parking brake handle, chrome cup holder trim, and trunk lid cover with running pony emblem.