Grindoce is almost a complete shoot-off of hardcore and crust.
D.R.I. (a hardcore band) recorded the first blastbeat in '82/83 with the song So Sence on the Dirty Rotten LP.
Crass, Discharge were also heavily influencial to grindcore. Discharge coined the term "noise not music", That pretty much sums up grindcore. Extreme Noise Terror also did a split with Chaos UK.
Napalm Death also started off as an anarcho band, later they turned into a crust, then thrash (not like thresh metal, more like Heresy), then later grindcore with the second side of Scum.
Anyways, there's some pretty good hardcore around today, check out Six Weeks Records, or hardcorehalocaust.com.
Municipal Waste, Holier Than Thou? & World Burns To Death, go check them out.