Is European Commission accountable to elected MEPs?

Just commented on The Undemocratic EU Explained - It Will Never Change
(by Get Out activist from Centre for European Reform, Huffington Post, 21/03/2016), as follows:
You say "Theoretically, the Parliament has the ability to remove the Commission; however the Parliament has never successfully been able to remove it." Glad you acknowledge that the Commission is accountable to elected MEPs. It's not just theoretical, however: MEPs have used such powers, as for example on 18 November 2004 when Commission President Jose Manuel Barroso had to withdraw his original line-up after MEPs objected to the views on women and homosexuality of Italian nominee Rocco Buttiglione.

Here is a summary from the (usually reliable) House of Commons Library in The European Union: a democratic institution? (2014) at section 3.2:

Since 1986 the Member States have agreed through Treaty changes to give the European Parliament (EP) more legislative power:

• The Single European Act of 1986 helped redress the institutional balance by giving the EP a second reading. Under the ‘cooperation procedure’, the Council could only approve a previously rejected proposal by a unanimous vote rather than by a qualified majority. Also, the EP received the right to veto the accession of new Member States and assent with the Council to international agreements.

• The Maastricht Treaty introduced co-decision and gave the EP an ultimate right to veto a legislative proposal by an absolute majority after two readings of the Council and EP. 

• The Amsterdam and Nice Treaties extended the use of co-decision, giving the EP a say in a wider range of matters. The Nice Treaty gave the EP the right to institute proceedings before the ECJ seeking to review acts of the institutions 

• The Lisbon Treaty made co-decision (renamed the Ordinary Legislative Procedure - OLP) the EU’s default decision-making procedure and extended it to justice and home affairs areas such as immigration, offences and penalties, police cooperation and aspects of trade and agriculture policy. The EP gained almost equal rights with the Council in the adoption of legislation. 

• Lisbon abolished the distinction between ‘compulsory’ and ‘non-compulsory’ expenditure, so that now the EP and Council determine all EU expenditure together. 

• The EP has also ‘democratised’ through soft powers, such as its right, by a two-thirds majority, to pass a motion of censure against the Commission, to question the Commission and Council at a regular question time and establish committees of inquiry to investigate cases of poor administration by the EU institutions.