I will attempt to present factors that have contributed to the Oakland Raiders' disappointments since reaching the Super Bowl during the 2002 season, then use it as a snapshot to compare to a relative snapshot of Raiders teams in the 70s-80s. This is not meant to serve as a comprehensive or definitive list, but as a perspective.
Coaching
Since the Raiders' 2002 season, in which they reached the Super Bowl, the Oakland Raiders have had seven different individuals serve as head coach: Bill Callahan, Norv Turner, Art Shell, Lane Kiffin, Tom Cable, Hue Jackson, and Dennis Green.
A constant change in higher-level personnel does not promote positive team culture and consistency.
Take the San Francisco 49ers between 2005-2010 for example. QB Alex Smith played for a different offensive coordinator each year and a coach in Mike Singletary who lost his players early on during his tenure as head coach. It wasn't until Jim Harbaugh began his tenure in head coach at San Francisco in 2011 that team culture improved and Alex Smith's (and his team's) strengths were utilized properly, leading to an NFC Championship and Super Bowl appearance in Harbaugh's first two seasons as 49ers head coach respectively.
If they can bring in the right personnel to improve team culture and utilize the team's strengths, the Oakland Raiders may find themselves to be a formidable contender.
Front Office
Several front office moves have not worked out in the favor of the Oakland Raiders. Here is an investigation of a few (of many).
Randy Moss
A 7x Pro Bowl selection with 156 TDs in his 14 year career, he managed only 11 TDs in Oakland during the 2005 and 2006 seasons. In comparison, Moss set the record for most receiving TDs as part of the New England Patriots with 23 during the 2007 season.
This suggests the Oakland Raiders did not have the players or coaches to utilize Moss to his full potential during his time there. His QBs were mainly Kerry Collins and Aaron Brooks.
JaMarcus Russell
A QB with a strong arm, great size, and a great college record, Russell was drafted first in the 2007 NFL Draft. Unfortunately, his work ethic and poor play led to his exit from the NFL after only three seasons.
Carson Palmer
Unwilling to play in Cincinatti, Palmer refused to attend training camp before the 2011 season. However, after Jason Campbell was injured during a game during the 2011 season, the Raiders traded a first round pick in 2012 and a second round pick in 2013 for Palmer. For a declining quarterback, this may have proven to be a costly move.
The examples above were not necessarily bad moves...but it does suggest that the Oakland Raiders must have a more developed team (offensive line to protect the QB and give the RB gaps to run through, defensive help, etc.) to contend beyond the regular season with the players they have.
Management
From 1972 up to his death in 2011, Al Davis served as owner and general manager of the Oakland Raiders. He played a significant part during the AFL-NFL merger. He was known to be one of the more hands-on owners in the NFL.
His hands-on ways contributed to the aforementioned coaching carousel and front office transactions since 2002. For example, Lane Kiffin did not want to draft JaMarcus Russell and this is one reason that led to his eventual dismissal as head coach. (1)
To sum it up, a collection of factors (coaching/team culture, players/team development, etc.) and ineffective/changing management has contributed to the Oakland Raiders' disappointments since 2002.
Comparing the teams of the 70s-80s to modern teams
The Oakland Raiders had two accomplished coaches during this time: John Madden and Tom Flores. They also had three accomplished QBs: Daryle Lamonica, Ken Stabler, and Jim Plunkett. This combination combined for three Super Bowls in 1976, 1980, and 1983 and eight divisional championships. In fact, Ken Stabler (2) is the only player from the All-1970s team and Jim Plunkett (3) is the only (retired) player to have won two Super Bowls as a starting QB and not be in the Hall of Fame.
As a result, one could surmise that the 70s-80s Oakland Raiders teams had consistency in higher-level personnel, positive team culture, role players, effective team development, and (although Al Davis had similar tendencies during the 70s-80s...ie) Ken Stabler and Marcus Allen) effective management.