Corporate infighting, incompetent sales, and misaligned vision pervaded the culture. It didn't help that PPro came out of left field and took everybody by surprise
When I interviewed at Intel in '95, they were absolutely giddy with how they stole Alpha's thunder. DEC was a better geographic choice for me, and, well...
HP didn't come into the picture until long after - DEC sold to Compaq in '98, Compaq to HP in '02. The race was over at least 7 years before that.
Edit: Not to mention the absolutely hostile stance DEC took to MS wrt NT. Due to Cutler's involvement with NT, DEC sued MSFT and somehow thought that would make MSFT become a loyal partner.
I remember Office 97 performing terribly on Alpha. We sent a compiler guy there to figure out why; turns out the Office team had a single Alpha in their pipeline, set to compile -O0, and pretty much said "this is there to check the lawsuit checkmark"