If you don't want to /can't install any additional software, there is a built-in way of looking up process IDs and apps: ps.
ps is a useful command line tool to find info on running processes. To find a particular app given the process number (which I've assigned to a variable myProcessId):
do shell script "ps -p " & myProcessId
this will return a result like this
PID TTY TIME CMD
66766 ?? 9:17.66 /Applications/Firefox.app/Contents/MacOS/firefox-bin -psn_0_3793822
to restrict the result to just the relevant line, pipe it to grep like so
do shell script "ps -p " & myProcessId & "|grep " & myProcessId
By parsing the answer you can find the name of the app. This might be a little tricky because the result will show the actual command used for the app, not the app name (if you look at the example you'll see it is possible to find it by looking for something.app in the result).
Edit - sorry, I misunderstood the question.
You can do it with system events (turns out to be much easier than faffing around with the shell anyway):
tell application "System Events"
set theprocs to every process whose unix id is myProcessId
repeat with proc in theprocs
set the frontmost of proc to true
end repeat
end tell