Hard drive replacement will not be a great deal since there are readily available guides that can help you perform a safe replacement. However, your Time Machine data (troubled Time Machine actually) sounds to be of great concern. You mentioned:
“I connected my Time Machine external hard drive to MBP, it didn’t worked properly. Tired with another Mac but no luck..”
What exactly happened to the Time Machine disk? Were you able to perform a Disk Utility Verify / Repair on separate macOS Yosemite 10.10 and below versions? If you are running macOS 10.11 or 10.12 then you can only repair (not verify) the Time Machine external hard drive.
Also, let know if your Time Machine external hard drive have components failed already or about to get failed. You can monitor your hard drive if the media is producing a strange sound such as clicking noise, buzzing, ticking likewise.
Unable to Mount the Time Machine (as it appears in the Disk Utility)
You can download a data recovery software that supports Time Machine data recovery and scan the external media for recovering deleted or inaccessible backup files. The software will be able to get hold of backups if the external hard drive has logical but not physical errors. If you can retrieve the data from the Time Machine successfully, then you can later restore it on your Mac’s new hard drive. Hope this helps.