Hello,
try this: I changed you condition only:
<% if (ValidationHelper.GetString(Eval("Link"),"").Contains("brightcove"))
{ %>
<li class="sixcol sixcol-small<%# ((DisplayIndex)%2==0 ? " first" : "") %>">
<a href="<%# Eval("Link") %>" onclick="window.open(this.href,'video','top=50, left=50, width=800, height=500, toolbar=no, menubar=no, location=no, scrollbars=no, resizable=no'); return false;" class="video-thumb" title="<%# Eval("Name") %>">
<img src="/chamberlain/media/library/images/blank.gif" alt="<%# Eval("Name") %>" />
<a class="video-title video-link" href="<%# Eval("Link") %>" onclick="window.open(this.href,'video','top=50, left=50, width=800, height=500, toolbar=no, menubar=no, location=no, scrollbars=no, resizable=no'); return false;" title="<%# Eval("Name") %>">
<%# Eval("Name") %>
<% }
else { %>
<li class="sixcol sixcol-small<%# ((DisplayIndex)%2==0 ? " first" : "") %>">
<a href="<%# Eval("Link") %>" class="video-thumb fancybox-video" title="<%# Eval("Name") %>">
<img src="/chamberlain/media/library/images/blank.gif" alt="<%# Eval("Name") %>" />
<a class="video-title video-link fancybox-video" href="<%# Eval("Link") %>" title="<%# Eval("Name") %>">
<%# Eval("Name") %>
<% } %>
If this doesn't help, paste here your error with stack trace.
BTW. Why you use html element "a" insinde another "a" ? It's not correct.