No not unless the Xbox is already modded - if it is not modded it will only run MS signed discs ie. original Xbox games' discs. However it is worth trying cold booting an installer disc like AID (Auto Installer Deluxe) or HeXEn (Heimdall's Xbox Engineering disc). That must be burned to DVD-R, preferably using ImgBurn at default settings: "Write image file to disc".
How were you trying to mod it? Softmod, chip or TSOP? I'd guess a softmod and if so you must have been using an MS original disc and one correct for your region. If you were not there is the cause of your problem.
So, if it was a softmod attempt, what exploit/installer were you using ie. Splinter Cell, 007 AUF, Mechassault, TH4 with Softmod Installer Deluxe (SID) or Rocky5's Xbox Softmodding Tool? Both those installer packages include the exploits and the installer. In fact Rocky5's includes TH4 (Tony Hawk Pro Skater 4) which is not provided in any other package as far as I know.
At what point in the process did the softmod fail?
If it is a bad softmod attempt then the reinstall of the MS dash cold booting an original game disc with a dashupdate included can leave behind remains of the earlier softmod. This can interfere with new attempts at softmodding. You must remove the existing exploit/installer game saves and freshly reinstall them. Even then it might not work.
If that happens then you should try using a different exploit ie. if you used Splinter Cell previously use 007 AUF instead and preferably a different installer too.
One important thing is to get the eeprom from the Xbox as a priority. If you can get an installer dash to load use the backup tool provided to get the eeprom and back it up to external storage ASAP.
The installer dash should also allow FTP access. That can be unreliable but you can use it to back up the eeprom to PC and gives you other modding options if softmodding does not work.