Other than the video card. For example the machine could have other issues.
http://compreviews.about.com/od/budgetdesk/gr/AcerAspireE360.htm shows it is about 4 years old so maybe something like this box can let you use your monitor? -> http://www.walmart.com/ip/eMachines-320-GB-EL1333G-01w/13352324
If the motherboard gave out then the cost of that plus the windows OS could exceed the next machine's cost.
I have an Acer Aspire E360 and the monitor died. I can connect it to another machine and it works just fine leading me to believe that it must be the video card. When I go inside the machine it appears that the video input is interfaced with the motherboard. I'm at a loss here and any advice would be greatly appreciated. It's tough diagnosing a problem with no monitor. If a video card were present, I would simply replace it.