In this paper we refer to the Open Web to the set of services offered freely to Internet users, representing a pillar of modern societies. Despite its importance for society, it is unknown how the COVID-19 pandemic is affecting the Open Web. In this paper, we address this issue, focusing our analysis on Spain, one of the countries which have been most impacted by the pandemic. On the one hand, we study the impact of the pandemic in the financial backbone of the Open Web, the online advertising business. To this end, we leverage concepts from Supply-Demand economic theory to perform a careful analysis of the elasticity in the supply of ad-spaces to the financial shortage of the online advertising business and its subsequent reduction in ad spaces' price. On the other hand, we analyze the distribution of the Open Web composition across business categories and its evolution during the COVID-19 pandemic. These analyses are conducted between Jan 1st and Dec 31st, 2020, using a reference dataset comprising information from more than 18 billion ad spaces. Our results indicate that the Open Web has experienced a moderate shift in its composition across business categories. However, this change is not produced by the financial shortage of the online advertising business, because as our analysis shows, the Open Web's supply of ad spaces is inelastic (i.e., insensitive) to the sustained low-price of ad spaces during the pandemic. Instead, existing evidence suggests that the reported shift in the Open Web composition is likely due to the change in the users' online behavior (e.g., browsing and mobile apps utilization patterns).