My eMachines (T3406) was working fine. Moved to another house and now monitor light flashes but no image. Computer hard drive making a lot of noise like it is booting but not finishing. It's an old style monitor. (Only use this for word processing etc, have tablet for internet)
The move probably damaged the computer. Either the vibrations and such that occurred during the move unseated some of the socketed circuits, or they damaged the hard drive. You need to take the cover off, press down into their connectors all the integrated circuit chips and memory sticks, and make sure all the connectors are properly connected, including to the disc drive(s). Also, remove and re-install all the PCI bus cards, such as the video card, et al.
If all that doesn't work, then find someone with a computer that works with a docking bay. Remove your hard drive, install it in the docking bay, and see if they can access the drive. If so, then the problem is the computer and not the drive, and your data should be recoverable.
FWIW, people pay me $100-$200 USD per hour to do this sort of thing... Care is needed to avoid causing additional damage. I have been trained in computer repair by IBM, Apple, Zenith, AT&T, Compaq, HP, and others (and have the paperwork to prove it - plus I am an electrical engineer), so it is something I know a little about. So, if you aren't certain that this is in your capability, take the system to a repair shop that specializes in PC repairs and service, and that has a good reputation. A lot of these may not be so good as their advertising would make you think. I have a small, local, PC shop that I use - they built my current workstation some years ago, to my specifications, and are very good.