The iMac died in what way? The hard drive died? Replacing the hard drive, while difficult would more than likely be much cheaper than even buying a cheapo Windows machine.
You can read/write via ethernet to a Time Capsule via a Windows machine.
You'll need to install the Windows Airport utility -
here - as long as you know your TC password.
However, you're going to need a Mac with Time Machine to be able to open and see the data (in any sort of meaningful way) in a Time Machine backup. You could then copy the data you want to a separate drive or to a separate folder on the TC.
Do not make any changes to the sparsebundle package or it will likely not work properly when you want to attempt a restore to another Mac.
(Also, it is better to ask to move a post to the correct forum than to create a 2nd identical post. Thanks)