I'm looking some bands, mostly Garage Punk bands. Bands that have that Motorhead & MC5 sound kicked to a fast Hardcore Punk speed.
Some bands I know like this include Gluecifer, Electric Frankenstein, Flamethrower, Supersuckers, Zeke, The Hookers, The hellacopters, & Turbonegro.

The Stooges, Sir Lord Baltimore, Budgie, The Cult, Black Flag, Mudhoney, Melvins (some songs are catchy punk oriented hard rock, otherwise most of their materials are sludge/doom), Valient Thorr etc. are very similar to the style you're looking for.

I'm already familiar to all those bands & they all sound nothing like what I'm looking for.

Well, to me they sound pretty similar to the sound you've described. To each his own I guess.

*edit. Derp, should have read more carefully

How about Dwarves?

Inepsy man. Inepsy
http://www.youtube.com/watch?v=y8LscrSOdvk

Speedwolf! Heavy/thrash with rock and roll and some punk influences. Huge Motorhead vibe.

These are good recomendations, but I want to clarify that I'm looking for Fast hardcore-ish speed layered on top of of a classic Rock structure. Something that sounds like 60's/70's Hard Rock/Metal, but with a punk like speed. As impressive as Speedwolf sounds, they have a more 80's feel due to the strong Thrash element.

Man, Zeke are probably my favorite band ever but I don't really know anyone other than those you mentioned that really apes that sound. If you know Zeke then you probably already know REO Speedealer and just didn't mention them in the OP but if you don't then you should check them out, they should be right up your alley.

Here's some other bands worth checking... I don't think any of them really fit what you're looking for 100% but their worth a listen.

Annihilation Time - Lots of Sabbath influence in the riffs, a lot of their stuff is more mid tempo but still rad.
http://downloads.tankcrimes.com/album/ii

The Shrine - Kinda along the same lines as Annihilation Time but with more emphasis on the 'rock' as opposed to 'punk'.
http://theshrine.bandcamp.com/album/primitive-blast

The Impalers - Strong Motorhead vibe from these dudes.
http://theimpalers.bandcamp.com/album/demo-2010

How 'bout some Artimus Pyledriver. Here's a sample:

what you want to hear is Puffball - esp. their album "SixPack to go" (but the other albums are good was well)

http://www.youtube.com/watch?v=HqACq-1AIy4
http://www.youtube.com/watch?v=ZGhKe41ThbE

The earlier Supersuckers stuff, like "The Smoke of Hell".

Many will disagree, but you might enjoy earlier Girlschool stuff, esepcially Demolition Boys LP.

Nebula's "So It Goes" really had what I was looking for.

Metal that really counts...

As lemmy would say, do not do heavy metal or punk, this is ROCK AND ROLL

What about Kvelertak? They are basically Turbonegro rip-off with some norwegian black metal influence.

Also check out Total 13 by Backyard Babies.