A capacitor is blown in the phone. Ace is right about just buying refurbished phones. I also recommend switching them to 53xx series if possible.
We are still only on version 2.3.6.73. Will my system support 53xx series phones?
No... 53xx phones are not supported until 3.2 or 4.0 (can't remember exactly).
You should really get current, your software is at least 10, maybe even 12+ years old... You will have to renew your software assurance with Mitel (contact your dealer) and then have your dealer upgrade you to current. All hardware should be compatible up to 6.1, although depending on your CF card you might have to replace it.
To be honest though, since the hardware is 10+ years old you may want to just go ahead and upgrade to a new HX chassis and the latest 6.2 software. Your old CS chassis has been discontinued and is no longer supported for newer software releases. Replacing the chassis with a new one will basically give you another 10-15 of usable life from your system and allow for newer devices, conference bridge, mobile twinning, Vmail to Email with hosted service, etc. You can reuse your old licenses and devices so the cost will be significantly less than a new system.
Although your existing system may run as is for years, it is a ticking time bomb and will fail eventually... 7-10 years is considered the typical lifespan of modern phone system hardware.